\r\n\tHydroxyapatite (HA) is an important member of the calcium phosphate chemical family. It has been used in several medical applications for the past decades, due to its chemical similarity to the mineral phase of bone and high biocompatibility. Several studies demonstrated that bone mineral presents several ion substitutions, so in order to prepare a synthetic material with an even closer composition to bone mineral, HA has been prepared with the incorporation of several ions like, silicon or fluoride. These ions induced not only structural changes on HA lattice, but also on its biocompatibility. \r\n\tSignificant advances in nanotechnologies resulted in the preparation of HA in different forms, with a wider range of applications, from support to drug and gene delivery. \r\n\tThis book aims to collect the most relevant information regarding HA properties, modifications and its application in the biomedical field.
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\n
1. Background
\n
Shannon [1] introduced the concept of entropy in communication theory and founded the subject of information theory. The stochastic system has an important property known as entropy which is widely used in various fields.
\n
Further, the second law of thermodynamics that explains that there cannot be spontaneous decrease in the entropy of system described that over time the systems tend to be more disordered. Thus, information theory has found wide applications in statistics, information processing and computing instead of concerned with communication systems only.
\n
If we consider entropy equivalent to uncertainty then an enormous deal of insight can be obtained. Zadeh [2] introduced and enlightened about a generalised theory of vagueness or ambiguity. In order to observe about the external world, uncertainty plays a very important role. For understanding composite phenomena, any discipline that contributes in order to understand measure, regulate, maximise or minimise and control is considered as a significant input.
\n
Uncertainty plays a significant role in our perceptions about the external world. Any discipline that can assist us in understanding it, measuring it, regulating it, maximizing or minimizing it and ultimately controlling it to the extent possible, should certainly be considered an important contribution to our scientific understanding of complex phenomena.
\n
Uncertainty is not a single monolithic concept. It can appear in several guises. It can arise in what we normally consider a probabilistic phenomenon. On the other hand, it can also appear in a deterministic phenomenon where we know that the outcome is not a chance event, but we are fuzzy about the possibility of the specific outcome. This type of uncertainty arising out of fuzziness is the subject of investigation of the relatively new discipline of fuzzy set theory.
\n
We shall first take up the case of probabilistic uncertainty. Probabilistic uncertainty is related to the uncertainty connected with the probability of outcomes.
\n
Consider a set of events E = (E1, E2,…, En)\n with a set of probability distribution P = (p1, p2, …,pn), pi ≥ 0, \n\n\n∑\n\ni\n=\n1\n\nn\n\n\np\ni\n\n=\n1\n\n.
\n
Then the Shannon [1] entropy associated with P is given by,
The base of logarithm is taken as 2. Also it is assumed that
\n
\n\n0\n\nlog0\n=\n0\n.\n\n
\n
Shannon [1] obtained (Eq. (1)) on the basis of following postulates:
H(P) should be a continuous permutationally symmetric function of p1, p2,…, pn, that is, ambiguity changes by slight quantity if there is slight quantity changes in pi’s and ambiguity remain unchanged if pi’s exchange among themselves.
H(p1, p2,…, pn, 0) = H(p1, p2,…, pn), that is, uncertainty should not change when an impossible outcome is added to the scheme.
H(P) should be minimum when P is any one of the n degenerate distribution \n\n\nΔ\n1\n\n=\n\n1\n0\n…\n0\n\n,\n\nΔ\n2\n\n=\n\n0\n1\n…\n0\n\n,\n…\n,\n\nΔ\nn\n\n=\n\n0\n0\n…\n1\n\n\n and the minimum value should be zero because in all these cases, there is no uncertainty about the outcome.
H(P) should be maximum when p1 = p2 = … = pn = 1/n because in this case the uncertainty is maximum.
H(P*Q) = H(P) + H(Q), that is, the uncertainty of two independent probability distributions is the sum of the uncertainties of the two probability distributions.
The measures in (Eq. (1)) not only measures uncertainty, but it also measures equality of p1, p2,…, pn, since it has the maximum value when p1, p2,…,pn, are all equal and has the minimum value when pi’s are most unequal. In fact pi’s can be regarded as proportions rather than probabilities.
\n
After Shannon’s [1] entropy, various other measures of entropy have been proposed.
\n
Entropy of order α was described by Renyi [3] in the way as:
Zadeh [2] introduced fuzzy set theory which is associated with vagueness arising in human cognitive methods. The alteration for an element connecting membership and nonmembership in the universe of classical sets is abrupt whereas in the universe of fuzzy sets the transition is gradual. Thus, the membership function describes the vagueness and ambiguity of an element and takes values in the interval [0, 1].
\n
Kapur [7] explained the concept of fuzzy entropy by considering the following vector \n\n\n\n\nμ\nA\n\n\n\nx\n1\n\n\n\n\n\nμ\nA\n\n\n\nx\n2\n\n\n\n…\n\n\nμ\nA\n\n\n\nx\nn\n\n\n\n\n\n.
\n
If \n\n\nμ\nA\n\n\n\nx\ni\n\n\n=\n0\n\n then the ith element does not belong to set A and if \n\n\nμ\nA\n\n\n\nx\ni\n\n\n=\n1\n\n, then the ith element belongs to set A. If \n\n\nμ\nA\n\n\n\nx\ni\n\n\n=\n0.5\n\n then highest ambiguity arises as to ith element belongs to set A or not. Thus, \n\n\n\n\nμ\nA\n\n\n\nx\n1\n\n\n\n\n\nμ\nA\n\n\n\nx\n2\n\n\n\n…\n\n\nμ\nA\n\n\n\nx\nn\n\n\n\n\n\n is termed as fuzzy vector and the set A is identified as the fuzzy set. Thus crisp set are those sets in which each element is 0 or 1 and hence uncertainty does not arise in these sets whereas those sets in which elements are 0 or 1 and others lie among 0 and 1 are entitled as fuzzy sets. A fuzzy set A is represented as A = \n\n\n\n\nx\ni\n\n\n\nμ\nA\n\n\n\nx\ni\n\n\n\n\n\ni\n=\n1\n\n2\n…\nn\n\n\n where \n\n\nμ\nA\n\n\n\nx\ni\n\n\n\n gives the degree of belongingness of the element \n\n\n\nx\ni\n\n\n\n to A. We explain the concept of membership function \n\n\nμ\nA\n\n\n:X\n\n→\n\n0\n1\n\n\n as follows:
\n
\n\n\nμ\nA\n\n\n\nx\ni\n\n\n=\n\n\n\n\n\n0\n,\n\nif\n\nx\n∉\nA\n\nand\n\nthere is\n\nno\n\nambiguity\n\n\n\n\n1\n,\n\nif\n\nx\n∈\nA\n\nand\n\nthere is\n\nno\n\nambiguity\n\n\n\n\n0.5\n,\n\nif there is\n\nmax\nimum\n\nambiguity\n\nwhether\n\nx\n∉\nA\n\nx\n∈\nA\n\n\n\n\n\n\nE10
\n
Further if \n\n\nμ\nB\n\n\n\nx\ni\n\n\n\n = \n\n\nμ\nA\n\n\n\nx\ni\n\n\n\n either 1 − \n\n\nμ\nA\n\n\n\nx\ni\n\n\n\n or then fuzzy sets A and B are characterised as fuzzy equivalent sets. Also, without being fuzzy equivalent, two sets can have same entropy but it is obvious to have identical entropy for fuzzy equivalent sets. Now if all the membership values of class of fuzzy equivalent sets are less than or equal to 0.5 then that set is defined as standard fuzzy set.
\n
For any fuzzy set A* to be a sharpened version of set A the subsequent requirements has to be fulfilled:
Thus, when \n\n\nx\n1\n\n,\n\n\nx\n2\n\n,\n…\n,\n\nx\nn\n\n\n are components of universe of discourse then, \n\n\n\n\nμ\nA\n\n\n\nx\n1\n\n\n\n\n\nμ\nA\n\n\n\nx\n2\n\n\n\n…\n\n\nμ\nA\n\n\n\nx\nn\n\n\n\n\n\n are positioned among 0 and 1 but since their sum is not unity therefore they are not considered as probabilities. However,
When there is uncertainty due to fuzziness of information it is known as fuzzy entropy measures whereas when the uncertainty is due to information available in terms of probability distribution it is known as probabilistic entropy. Following similarities and dissimilarities are there between fuzzy entropy measures and probabilistic entropy measures:
0 ≤ \n\n\np\ni\n\n\n ≤ 1 for each i. Also 0 ≤ \n\n(\n\nμ\nA\n\n\n\nx\ni\n\n\n\n ≤ 1 for each i.
\n\n\n\n∑\n\ni\n=\n1\n\nn\n\n\np\ni\n\n=\n1\n\n for all probability distributions, but \n\n\n∑\n\ni\n=\n1\n\nn\n\n(\n\nμ\nA\n\n\n\nx\ni\n\n\n)\n\n need not be equal to unity and it need not even be the same for all fuzzy sets.
The probabilistic uncertainty measure measures how close the probability distribution (p1, p2, …, pn) is to the uniform distribution (1/n, 1/n, …, 1/n) and how far away it is from degenerate distributions. Fuzzy uncertainty measures how close the fuzzy distribution is from the most fuzzy vector distribution (1/2, 1/2, …, 1/2) and how far it is from the distribution of crisp sets.
\n\n\n(\n\nμ\nA\n\n\n\nx\ni\n\n\n)\n\n gives the same degree of fuzziness as 1 − \n\n(\n\nμ\nA\n\n\n\nx\ni\n\n\n)\n\n because both are equidistant from 1/2 and the crisp set values 0 and 1. However probabilities p and 1 − p make different contributions to probabilistic uncertainty. As such while most measures of fuzzy entropy are of the form \n\n\n∑\n\ni\n=\n1\n\nn\n\nf\n(\n\nμ\nA\n\n\n\nx\ni\n\n\n\n + \n\n\n∑\n\ni\n=\n1\n\nn\n\nf\n\n\n1\n−\n\nμ\nA\n\n\n\nx\ni\n\n\n\n\n\n, most measures of probabilities entropy are of the form \n\n\n∑\n\ni\n=\n1\n\nn\n\nf\n\n\np\ni\n\n\n\n. However some measures of probabilistic entropy can also be of the form \n\n\n∑\n\ni\n=\n1\n\nn\n\nf\n\n\np\ni\n\n\n\n + \n\n\n∑\n\ni\n=\n1\n\nn\n\nf\n\n\np\ni\n\n\n\n.
Similarly while many measures for fuzzy directed divergence are all of the form \n\n\n∑\n\ni\n=\n1\n\nn\n\nf\n(\n\nμ\nA\n\n\n\nx\ni\n\n\n,\n\n\nμ\nB\n\n\n\nx\ni\n\n\n+\n\n∑\n\ni\n=\n1\n\nn\n\nf\n\n\n1\n−\n\nμ\nA\n\n\n\nx\ni\n\n\n\n\n,\n\n\n\n1\n−\n\nμ\nB\n\n\n\nx\ni\n\n\n\n\n)\n\n, most of the probabilistic measures are of the form \n\n\n∑\n\ni\n=\n1\n\nn\n\nf\n\n\np\ni\n\n\n\n\nq\ni\n\n\n\n\n. For each measure of probabilistic entropy or directed divergence, we have a corresponding measure of fuzzy entropy and fuzzy directed divergence and vice-versa.
The common properties arise from the consideration that both types of measures are based on measures of distance from (1/n, 1/n, …, 1/n) in one case and from (1/2, 1/2, …, 1/2) in the other.
The dissimilarity arises because while \n\n\n∑\n\ni\n=\n1\n\nn\n\n\np\ni\n\n\n=\n1\n\n, \n\n\n∑\n\ni\n=\n1\n\nn\n\n(\n\nμ\nA\n\n\n\nx\ni\n\n\n\n is not 1. The probabilities of n − 1 outcomes will determine the probability of the nth outcome. However fuzziness of n elements of the fuzzy set are quite independent and our knowledge of fuzziness of n − 1 elements gives us no information about the fuzziness of the nth element.
Conceptually the two types of uncertainty are poles apart. One deals with probabilities or relative frequencies and repeated experiments, while the other deals with estimation of fuzzy values. The probabilities can be determined objectively and experimentally and should naturally be the same for everyone. Fuzziness is one’s perception of membership of an element of a set and can be subjective. However, after finding fuzzy value for every member of the set, everything else is objective. In probability theory also after assigning probabilities, everything is also objective.
Fuzzy and probabilistic entropies are concave functions of \n\n\n\n\nμ\nA\n\n\n\nx\n1\n\n\n\n\n\nμ\nA\n\n\n\nx\n2\n\n\n\n…\n\n\nμ\nA\n\n\n\nx\nn\n\n\n\n\n\n and p1, p2, …, pn respectively. If we start with any value of \n\n\n\n\nμ\nA\n\n\n\nx\n1\n\n\n\n\n\nμ\nA\n\n\n\nx\n2\n\n\n\n…\n\n\nμ\nA\n\n\n\nx\nn\n\n\n\n\n\n and approach the vector 1/2, 1/2, …, 1/2, the fuzzy entropy will increase. Similarly, if we start with any probability vector p1, p2, …, pn and approach the vector 1/n, 1/n, …, 1/n, the probabilistic entropy will increase. Thus, \n\nZ\n=\nF\n\n\n\nμ\nA\n\n\n\nx\n1\n\n\n\n\n\nμ\nA\n\n\n\nx\n2\n\n\n\n…\n\n\nμ\nA\n\n\n\nx\nn\n\n\n\n\n\n, where F is a fuzzy entropy is a concave surface with maximum value at 1/2, 1/2, …, 1/2. Similarly Z = G(p1, p2, …, pn) where G is probabilistic entropy is a concave surface with maximum value at 1/n, 1/n, …, 1/n.
\n
While processing information, making decision and in our language we can find fuzziness. Many authentic world objectives and human thinking consider uncertainty and fuzziness as their fundamental nature. Uncertainty and fuzziness are removed by the utilization of information. The degree of information is the quantity of uncertainty eliminated whereas the degree of vagueness and ambiguity of uncertainties is the quantity of fuzziness.
\n
The theory of fuzziness is related to various areas of research such as Statistics, Information theory, Clustering and Decision analysis, Medical and Socio-economic prediction, Image processing, etc. The preparation and analysis of information development method are the applications of the mathematical designs related to system research.
\n
In order to deal with fuzziness there is a small area from the extremely large fields of theories and applications which have been developed from the concept of fuzziness.
\n
We define problems in the form of decision, management and prediction and by analysis, understanding and utilization of information, we can find their solutions. Thus, a significant quantity of information together with significant quantity of uncertainty is considered as the ground of many problems.
\n
As we become aware of how much we know and how much we do not know, as information and uncertainty themselves become the focus of our concern, we begin to see our problems as centring on the issue of complexity.
\n
Thus, ambiguity due to fuzziness of information is calculated by fuzzy entropy whereas vagueness due to information which is accessible in context of probability distribution is computed by probabilistic entropy.
\n
Entropy theory was developed to measure uncertainty of a probability distribution and therefore it was natural for researchers in fuzzy set theory to make use of entropy concepts in measuring fuzziness.
\n
Entropy of a fuzzy set A having n support points was characterised by Kauffman [8] in the way as
Kosko [13] introduced fuzzy entropy and conditioning. Pal and Pal [14] gave object background segmentation using new definition of entropy. Parkash [15] proposed new measures of weighted fuzzy entropy and their applications for the study of maximum weighted fuzzy entropy principle. Parkash and Gandhi [16] suggested new generalised measures of fuzzy entropy and properties. Parkash and Singh [17] gave characterization of useful information theoretic measures. Taneja [18] introduced generalised information measures and their applications. Taneja and Tuteja [19] gave characterization of quantitative-qualitative measure of relative information. Tuteja [20] introduced characterization of nonadditive measures of relative information and accuracy. Tuteja and Hooda [21] proposed generalised useful information measure of type α and degree β. Tuteja and Jain [22, 23] gave characterization of relative useful information having utilities as monotone functions and an axiomatic characterization of relative useful information. Tahayori [24] presented a universal methodology for generating an interval type 2 fuzzy set membership function from a collection of type 1 fuzzy sets. Kumar and Bajaj [25] introduced NTV metric based entropies of interval-valued intuitionistic fuzzy sets and their applications in decision making.
\n
Mishra [26] introduced two exponential fuzzy information measures and characterised axiomatically. To show the effectiveness of the proposed measure, it is compared with the existing measures. Further, two fuzzy discrimination and symmetric discrimination measures are defined and their validity are checked. Important properties of new measures are studied and their applications in pattern recognition and diagnosis problem of crop disease are discussed. Hooda and Mishra [27] gave two sine and cosine trigonometric measures of fuzzy information and obtained new measures of trigonometric fuzzy information.
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\n
\n
3. A new parametric measure of fuzzy information measure involving two parameters \n\nα\n\n and \n\nβ\n\n\n
\n
A new generalised fuzzy information measure of order α and type β has been suggested and their necessary and required properties are examined. Thereafter, its validity is also verified. Also, the monotonic behaviour of fuzzy information measure of order α and type β has been conferred.
\n
The generalised measure of fuzzy information of order \n\nα\n\n and type \n\nβ\n\n is given by,
We have supposed that, \n\n\n0\n\n0\n.\nα\n\n\n=\n1\n\n, we study the following properties:
\n
Property 1: \n\n\nH\nα\nβ\n\n\nA\n\n≥\n0\n\n i.e. \n\n\nH\nα\nβ\n\n\nA\n\n\n is nonnegative.
\n
Property 2: \n\n\nH\nα\nβ\n\n\nA\n\n\n is minimum if A is a non-fuzzy set.
\n
For \n\n\nμ\nA\n\n\n\nx\ni\n\n\n=\n0\n\n, it implies \n\n\nH\nα\nβ\n\n\nA\n\n\n = 0 and \n\n\nμ\nA\n\n\n\nx\ni\n\n\n=\n0\n\n we have \n\n\nH\nα\nβ\n\n\nA\n\n\n = 0.
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Property 3: \n\n\nH\nα\nβ\n\n\nA\n\n\n is maximum if A is most fuzzy set.
\n
We have, \n\n\n\n∂\n\nH\nα\nβ\n\n\nA\n\n\n\n∂\n\nμ\nA\n\n\n\nx\ni\n\n\n\n\n=\n\nα\n\n1\n−\nα\n\n\n\n\n\n\n\n\n\nμ\nA\n\n\n\nx\ni\n\n\n\n\n\n\nαμ\nA\n\n\n\nx\ni\n\n\n\n\n+\n\n\n\n1\n−\n\nμ\nA\n\n\n\nx\ni\n\n\n\n\n\nα\n\n\n1\n−\n\nμ\nA\n\n\n\nx\ni\n\n\n\n\n\n\n\n\n\nβ\n−\n1\n\n\n\n\n\n\n\n\nμ\nA\n\n\n\nx\ni\n\n\n\n\n\n\nαμ\nA\n\n\n\nx\ni\n\n\n\n\n\n\n1\n+\nlog\n\nμ\nA\n\n\n\nx\ni\n\n\n\n\n−\n\n\n\n1\n−\n\nμ\nA\n\n\n\nx\ni\n\n\n\n\n\nα\n\n\n1\n−\n\nμ\nA\n\n\n\nx\ni\n\n\n\n\n\n\n(\n1\n+\nlog\n\n\n1\n−\n\nμ\nA\n\n\n\nx\ni\n\n\n\n\n\n\n\n.
\n
Taking, \n\n\n\n∂\n\nH\nα\nβ\n\n\nA\n\n\n\n∂\n\nμ\nA\n\n\n\nx\ni\n\n\n\n\n=\n\n 0 which is possible \n\n\nμ\nA\n\n\n\nx\ni\n\n\n=\n1\n−\n\nμ\nA\n\n\n\nx\ni\n\n\n\n that is if \n\n\nμ\nA\n\n\n\nx\ni\n\n\n=\n\n1\n2\n\n\n.
\n
Now, we have, \n\n\n\n\n∂\n2\n\n\nH\nα\nβ\n\n\nA\n\n\n\n\n∂\n2\n\n\nμ\nA\n\n\n\nx\ni\n\n\n\n\n\n, Thus, at \n\n\nμ\nA\n\n\n\nx\ni\n\n\n=\n\n1\n\n2\n.\n\n\n\n
When \n\n\nμ\nA\n\n\n\nx\ni\n\n\n\n lies between 0 and 1/2 then \n\n\nH\nα\nβ\n\n\nA\n\n\n is an increasing function whereas when \n\n\nμ\nA\n\n\n\nx\ni\n\n\n\n lies between 1/2 and 1 then \n\n\nH\nα\nβ\n\n\nA\n\n\n is a decreasing function of \n\n\nμ\nA\n\n\n\nx\ni\n\n\n\n
\n
Let \n\n\nA\n∗\n\n\n be sharpened version of A which means that
If \n\n\nμ\nA\n\n\n\nx\ni\n\n\n<\n0.5\n\n then \n\n\nμ\n\nA\n∗\n\n\n\n\nx\ni\n\n\n≤\n\nμ\nA\n\n\n\nx\ni\n\n\n\n for all i = 1, 2, …, n
If \n\n\nμ\nA\n\n\n\nx\ni\n\n\n>\n0.5\n\n then \n\n\nμ\n\nA\n∗\n\n\n\n\nx\ni\n\n\n≥\n\nμ\nA\n\n\n\nx\ni\n\n\n\n for all i = 1, 2, …, n
\n
Since \n\n\nH\nα\nβ\n\n\nA\n\n\n is an increasing function of \n\n\nμ\nA\n\n\n\nx\ni\n\n\n\n for \n\n0\n≤\n\nμ\nA\n\n\n\nx\ni\n\n\n≤\n\n1\n2\n\n\n and decreasing function of \n\n\nμ\nA\n\n\n\nx\ni\n\n\n\n for \n\n\n1\n2\n\n≤\n\nμ\nA\n\n\n\nx\ni\n\n\n≤\n\n 1, therefore
\n\n\n\nμ\n\nA\n∗\n\n\n\n\nx\ni\n\n\n≤\n\nμ\nA\n\n\n\nx\ni\n\n\n\n this implies \n\n\nH\nα\nβ\n\n\n\nA\n∗\n\n\n≤\n\nH\nα\nβ\n\n\nA\n\n\n in [0, 0.5]
\n\n\n\nμ\n\nA\n∗\n\n\n\n\nx\ni\n\n\n≤\n\nμ\nA\n\n\n\nx\ni\n\n\n\n this implies \n\n\nH\nα\nβ\n\n\n\nA\n∗\n\n\n≤\n\nH\nα\nβ\n\n\nA\n\n\n in [0.5, 1]
Property 5: \n\n\nH\nα\nβ\n\n\nA\n\n=\n\nH\nα\nβ\n\n\n\nA\n¯\n\n\n\n, where \n\n\nA\n¯\n\n\n is the compliment of A i.e. \n\n\nμ\nA\n\n\n\nx\ni\n\n\n\n= 1 - \n\n\nμ\nA\n\n\n\nx\ni\n\n\n\n.
\n
Thus when \n\n\nμ\nA\n\n\n\nx\ni\n\n\n\n is varied to (1 − \n\n\nμ\nA\n\n\n\nx\ni\n\n\n\n) then \n\n\nH\nα\nβ\n\n\nA\n\n\n does not change.
\n
Under the above conditions, the generalised measure proposed in (26) is a valid measure of fuzzy information measure.
\n
\n
\n
3.2. Monotonic behaviour of fuzzy information measure
\n
In this section we study the monotonic behaviour of the fuzzy information measure. For this, diverse values of \n\n\nH\nα\nβ\n\n\nA\n\n\n by assigning various values to \n\nα\n\n and \n\nβ\n\n has been calculated and further the generalised measure has been presented graphically.
\n
Case I: For \n\nα\n\n > 1, \n\nβ\n\n =1, we have compiled the values of \n\n\nH\nα\nβ\n\n\nA\n\n\n in Table 1, (a) and presented the fuzzy entropy in Figure 1(a) which unambiguously illustrates that the fuzzy information measure is a concave function.
\n
\n
\n
\n
\n
\n
\n
\n\n
\n
\n\n\n\nμ\nA\n\n\n\nx\ni\n\n\n\n\n
\n
\n\n\n\nH\n\nα\n\n\nβ\n\n\n\nA\n\n\n\n
\n
\n\n\n\nμ\nA\n\n\n\nx\ni\n\n\n\n\n
\n
\n\n\n\nH\n\nα\n\n\nβ\n\n\n\nA\n\n\n\n
\n
\n\n\n\nμ\nA\n\n\n\nx\ni\n\n\n\n\n
\n
\n\n\n\nH\n\nα\n\n\nβ\n\n\n\nA\n\n\n\n
\n
\n\n\n
\n
0.0
\n
0.0
\n
0.0
\n
0.0
\n
0.0
\n
0.0
\n
\n
\n
0.1
\n
0.5419
\n
0.1
\n
0.5074
\n
0.1
\n
2.0337
\n
\n
\n
0.2
\n
0.7749
\n
0.2
\n
0.7763
\n
0.2
\n
2.7289
\n
\n
\n
0.3
\n
0.9075
\n
0.3
\n
0.9534
\n
0.3
\n
3.0732
\n
\n
\n
0.4
\n
0.9778
\n
0.4
\n
1.0517
\n
0.4
\n
3.2411
\n
\n
\n
0.5
\n
1.0
\n
0.5
\n
1.0844
\n
0.5
\n
3.2916
\n
\n
\n
0.6
\n
0.9778
\n
0.6
\n
1.0517
\n
0.6
\n
3.2411
\n
\n
\n
0.7
\n
0.9075
\n
0.7
\n
0.9534
\n
0.7
\n
3.0732
\n
\n
\n
0.8
\n
0.7749
\n
0.8
\n
0.7763
\n
0.8
\n
2.7289
\n
\n
\n
0.9
\n
0.5419
\n
0.9
\n
0.5074
\n
0.9
\n
2.0337
\n
\n
\n
1.0
\n
0.0
\n
1.0
\n
0.0
\n
1.0
\n
0.0
\n
\n
\n
(a)
\n
(b)
\n
(c)
\n
\n\n
Table 1.
The values of fuzzy information measure for α = 2 and β = 1; α = 1.5 and β = 0.1; and α = 1.5 and β = 2.5.
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Figure 1.
Representation of the monotonic behaviour of fuzzy information measure for (a) For, α = 2 and β = 1; (b) For, α = 1.5 and β = 0.1; and (C) For, α = 1.5 and β = 2.5.
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For \n\nα\n\n = 2, \n\nβ\n\n = 1, values of \n\n\nH\nα\nβ\n\n\nA\n\n\n have been represented with the help of graph for α = 2 and β = 1 which implies that the proposed measure is a concave function. Similarly, for other values of α and β, we get different concave curves.
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Case II: For \n\nα\n\n > 1, 0 < \n\nβ\n\n < 1 we have compiled the values of \n\n\nH\nα\nβ\n\n\nA\n\n\n in Table 1, (b) and presented the fuzzy entropy in the Figure 1(b) which unambiguously illustrates that the fuzzy entropy is a concave function.
\n
For α = 1.5 and \n\nβ\n=\n\n 0.1, values of \n\n\nH\nα\nβ\n\n\nA\n\n\n have been represented with the help of graph for α = 1.5 and β = 0.1 which implies that the proposed measure is a concave function. Similarly, for other values of α and β, we get different concave curves.
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Case III: For \n\nα\n\n > 1, \n\nβ\n\n > 1 we have compiled the values of \n\n\nH\nα\nβ\n\n\nA\n\n\n in Table 1, (c) and presented the fuzzy entropy in Figure 1(c) which unambiguously illustrates that the fuzzy entropy is a concave function.
\n
For \n\nα\n\n = 1.5 and \n\nβ\n=\n\n 2.5, values of \n\n\nH\nα\nβ\n\n\nA\n\n\n have been represented with the help of graph for α = 1.5 and β = 2.5 which implies that the proposed measure is a concave function. Similarly, for other values of α and β, we get different concave curves.
\n
\n
\n
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4. A new parametric measure of fuzzy information measure involving three parameters \n\nα\n\n, \n\nβ\n\n and \n\nγ\n\n\n
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Further, a new generalised fuzzy information measure involving three parameters α, β and γ has been suggested and their necessary and required properties are examined. Thereafter, its validity is also verified. Also, the monotonic behaviour of fuzzy information measure of order α, β and γ has been introduced.
\n
The generalised measure of fuzzy information involving three parameters α, β and γ is given by,
4.1. Properties of \n\n\nH\n\nα\n,\nβ\n,\nγ\n\n\n\nA\n\n\n\n
\n
We have supposed that, \n\n\n0\n\n0\n.\nα\n\n\n=\n1\n\n, we study the following properties:
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Property 1: \n\n\nH\n\nα\n,\nβ\n,\nγ\n\n\n\nA\n\n≥\n0\n\n i.e. \n\n\nH\n\nα\n,\nβ\n,\nγ\n\n\n\nA\n\n\n is nonnegative.
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Property 2: \n\n\nH\n\nα\n,\nβ\n,\nγ\n\n\n\nA\n\n\n is minimum if A is a non-fuzzy set.
\n
for \n\n\nμ\nA\n\n\n\nx\ni\n\n\n=\n0\n\n, it implies \n\n\nH\n\nα\n,\nβ\n,\nγ\n\n\n\nA\n\n=\n0\n\n and \n\n\nμ\nA\n\n\n\nx\ni\n\n\n=\n1\n\n we have \n\n\nH\n\nα\n,\nβ\n,\nγ\n\n\n\nA\n\n=\n0\n\n.
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Property 3: \n\n\nH\n\nα\n,\nβ\n,\nγ\n\n\n\n\n\nA\n∗\n\n\n\n≤\n\nH\n\nα\n,\nβ\n,\nγ\n\n\n\nA\n\n\n, where \n\n\nA\n∗\n\n\n be sharpened version of A.
\n
When \n\n\nμ\nA\n\n\n\nx\ni\n\n\n\n lies between 0 and 1/2 then \n\n\nH\n\nα\n,\nβ\n,\nγ\n\n\n\nA\n\n\n is an increasing function whereas when \n\n\nμ\nA\n\n\n\nx\ni\n\n\n\n lies between 1/2 and 1 then \n\n\nH\n\nα\n,\nβ\n,\nγ\n\n\n\nA\n\n\n is a decreasing function of \n\n\nμ\nA\n\n\n\nx\ni\n\n\n\n
\n
Let \n\n\nA\n∗\n\n\n be sharpened version of A which means that
If \n\n\nμ\nA\n\n\n\nx\ni\n\n\n<\n0.5\n\n then \n\n\nμ\n\nA\n∗\n\n\n\n\nx\ni\n\n\n≤\n\nμ\nA\n\n\n\nx\ni\n\n\n\n for all i = 1, 2, …, n
If \n\n\nμ\nA\n\n\n\nx\ni\n\n\n>\n0.5\n\n then \n\n\nμ\n\nA\n∗\n\n\n\n\nx\ni\n\n\n≥\n\nμ\nA\n\n\n\nx\ni\n\n\n\n for all i = 1, 2, …, n
\n
Since \n\n\nH\n\nα\n,\nβ\n,\nγ\n\n\n\nA\n\n\n is an increasing function of \n\n\nμ\nA\n\n\n\nx\ni\n\n\n\n for \n\n0\n≤\n\nμ\nA\n\n\n\nx\ni\n\n\n≤\n\n1\n2\n\n\n and decreasing function of \n\n\nμ\nA\n\n\n\nx\ni\n\n\n\n for \n\n\n1\n2\n\n≤\n\nμ\nA\n\n\n\nx\ni\n\n\n≤\n\n 1, therefore
\n\n\n\nμ\n\nA\n∗\n\n\n\n\nx\ni\n\n\n≤\n\nμ\nA\n\n\n\nx\ni\n\n\n\n this implies \n\n\nH\n\nα\n,\nβ\n,\nγ\n\n\n\n\n\nA\n∗\n\n\n\n≤\n\nH\n\nα\n,\nβ\n,\nγ\n\n\n\nA\n\n\n in [0, 0.5]
\n\n\n\nμ\n\nA\n∗\n\n\n\n\nx\ni\n\n\n≤\n\nμ\nA\n\n\n\nx\ni\n\n\n\n this implies \n\n\nH\n\nα\n,\nβ\n,\nγ\n\n\n\n\n\nA\n∗\n\n\n\n≤\n\nH\n\nα\n,\nβ\n,\nγ\n\n\n\nA\n\n\n in [0.5, 1]
Property 4: \n\n\nH\n\nα\n,\nβ\n,\nγ\n\n\n\nA\n\n=\n\nH\n\nα\n,\nβ\n,\nγ\n\n\n\n\nA\n¯\n\n\n\n, where \n\n\n\nA\n¯\n\n\n\n is the compliment of A i.e. \n\n\nμ\nA\n\n\n\nx\ni\n\n\n=\n1\n−\n\nμ\nA\n\n\n\nx\ni\n\n\n\n
\n
Thus, when \n\n\nμ\nA\n\n\n\nx\ni\n\n\n\n is varied to 1 − \n\n\nμ\nA\n\n\n\nx\ni\n\n\n\nthen \n\n\nH\n\nα\n,\nβ\n,\nγ\n\n\n\nA\n\n\n does not change.
\n
Under the above conditions, the generalised measure proposed in (27) is a valid measure of fuzzy information measure.
\n
\n
\n
4.2. Monotonic behaviour of fuzzy information measure
\n
In this section we study the monotonic behaviour of the fuzzy information measure. For this, diverse values of \n\n\nH\n\nα\n,\nβ\n,\nγ\n\n\n\nA\n\n\n by assigning various values to α, β and γ have been calculated and further the generalised measure has been presented graphically.
\n
Case I: For α > 1, β = 2, γ = 3, we have compiled the values of \n\n\nH\n\nα\n,\nβ\n,\nγ\n\n\n\nA\n\n\n in Table 2, (a)–(e) and presented the fuzzy entropy in Figure 2(a)–(e) which unambiguously illustrates that the fuzzy information measure is a concave function. For α = 1.5, β = 2, γ = 3, values of \n\n\nH\n\nα\n,\nβ\n,\nγ\n\n\n\nA\n\n\n have been represented with the help of graph \n\nγ\n=\n3\n\n which implies that the proposed measure is a concave function. Similarly, for other values of α, β and γ we get different concave curves. Further it has been shown that \n\n\nH\n\nα\n,\nβ\n,\nγ\n\n\n\nA\n\n\n is a concave function obtaining its maximum value at \n\n\nμ\nA\n\n\n\nx\ni\n\n\n=\n\n1\n2\n\n\n. Hence \n\n\nH\n\nα\n,\nβ\n,\nγ\n\n\n\nA\n\n\n is increasing function of \n\n\nμ\nA\n\n\n\nx\ni\n\n\n\n in interval [0, 0.5) and decreasing function of \n\n\nμ\nA\n\n\n\nx\ni\n\n\n\n in interval (0.5, 1]. Similarly, for α = 2, β = 2 and γ = 3, α = 2.5, β = 2 and γ = 3, α = 3, β = 2 and γ = 3, α = 3.5, β = 2 and γ = 3, \n\nγ\n=\n3\n\n values of \n\n\nH\n\nα\n,\nβ\n,\nγ\n\n\n\nA\n\n\n have been represented with the help of graph which implies that the proposed measure is a concave function.
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n
\n\n
\n
\n\n\n\nμ\nA\n\n\n\nx\ni\n\n\n\n\n\n
\n
\n\n\n\nH\n\nα\n,\nβ\n,\nγ\n\n\n\nA\n\n\n\n
\n
\n\n\n\nμ\nA\n\n\n\nx\ni\n\n\n\n\n\n
\n
\n\n\n\nH\n\nα\n,\nβ\n,\nγ\n\n\n\nA\n\n\n\n
\n
\n\n\n\nμ\nA\n\n\n\nx\ni\n\n\n\n\n\n
\n
\n\n\n\nH\n\nα\n,\nβ\n,\nγ\n\n\n\nA\n\n\n\n
\n
\n\n\n\nμ\nA\n\n\n\nx\ni\n\n\n\n\n\n
\n
\n\n\n\nH\n\nα\n,\nβ\n,\nγ\n\n\n\nA\n\n\n\n
\n
\n\n\n\nμ\nA\n\n\n\nx\ni\n\n\n\n\n\n
\n
\n\n\n\nH\n\nα\n,\nβ\n,\nγ\n\n\n\nA\n\n\n\n
\n
\n\n\n
\n
0.0
\n
0.0
\n
0.0
\n
0.0
\n
0.0
\n
0.0
\n
0.0
\n
0.0
\n
0.0
\n
0.0
\n
\n
\n
0.1
\n
12.8444
\n
0.1
\n
6.7318
\n
0.1
\n
4.6517
\n
0.1
\n
3.5865
\n
0.1
\n
2.9316
\n
\n
\n
0.2
\n
14.7302
\n
0.2
\n
7.5514
\n
0.2
\n
5.1212
\n
0.2
\n
3.8867
\n
0.2
\n
3.1353
\n
\n
\n
0.3
\n
15.3147
\n
0.3
\n
7.7794
\n
0.3
\n
5.2385
\n
0.3
\n
3.9540
\n
0.3
\n
3.1762
\n
\n
\n
0.4
\n
15.5250
\n
0.4
\n
7.8559
\n
0.4
\n
5.2750
\n
0.4
\n
3.9734
\n
0.4
\n
3.1870
\n
\n
\n
0.5
\n
15.5795
\n
0.5
\n
7.875
\n
0.5
\n
5.2837
\n
0.5
\n
3.9779
\n
0.5
\n
3.1894
\n
\n
\n
0.6
\n
15.5250
\n
0.6
\n
7.8559
\n
0.6
\n
5.2750
\n
0.6
\n
3.9734
\n
0.6
\n
3.1870
\n
\n
\n
0.7
\n
15.3147
\n
0.7
\n
7.7794
\n
0.7
\n
5.2385
\n
0.7
\n
3.9540
\n
0.7
\n
3.1762
\n
\n
\n
0.8
\n
14.7302
\n
0.8
\n
7.5514
\n
0.8
\n
5.1212
\n
0.8
\n
3.8867
\n
0.8
\n
3.1353
\n
\n
\n
0.9
\n
12.8444
\n
0.9
\n
6.7318
\n
0.9
\n
4.6517
\n
0.9
\n
3.5865
\n
0.9
\n
2.9316
\n
\n
\n
1.0
\n
0.0
\n
1.0
\n
0.0
\n
1.0
\n
0.0
\n
1.0
\n
0.0
\n
1.0
\n
0.0
\n
\n
\n
(a)
\n
(b)
\n
(c)
\n
(d)
\n
(e)
\n
\n\n
Table 2.
The values of fuzzy information measure for α = 1.5, β = 2 and γ = 3; α = 2, β = 2 and γ = 3; α = 2.5, β = 2 and γ = 3; α = 3, β = 2 and γ = 3; and α = 3.5, β = 2 and γ = 3.
\n
Figure 2.
Representation of the monotonic behaviour of fuzzy information measure for (a) For, α = 1.5, β = 2 and γ = 3; (b) For, α = 2, β = 2 and γ = 3; (c) For, α = 2.5, β = 2 and γ = 3; (d) For, α = 3, β = 2 and γ = 3; (e) For, α = 3.5, β = 2 and γ = 3.
\n
Further it has been shown that \n\n\nH\n\nα\n,\nβ\n,\nγ\n\n\n\nA\n\n\n is a concave function obtaining its maximum value at \n\n\nμ\nA\n\n\n\nx\ni\n\n\n=\n\n1\n2\n\n\n. Hence \n\n\nH\n\nα\n,\nβ\n,\nγ\n\n\n\nA\n\n\n is increasing function of \n\n\nμ\nA\n\n\n\nx\ni\n\n\n\n in interval [0, 0.5) and decreasing function of \n\n\nμ\nA\n\n\n\nx\ni\n\n\n\n in interval (0.5, 1].
\n
\n
\n
\n
5. Conclusions
\n
In this chapter, after reviewing some literatures on measures of information for fuzzy sets, a new generalised fuzzy information measure involving two parameters α and β has been introduced.
\n
The necessary properties of the proposed measure have been verified and further it has been studied that the proposed measure is a concave function as it has shown monotonicity.
\n
Further, a new generalised fuzzy information measure involving three parameters α, β and γ has been suggested and their necessary and required properties are examined. Thereafter, its validity is also verified. Also, the monotonic behaviour of fuzzy information measure of order α, β and γ has been conferred.
\n
Fuzzy sets are indispensable in fuzzy system model and fuzzy system design, while the measurement of fuzziness in fuzzy sets is the fuzzy entropy or fuzzy information measure. Therefore, fuzzy information measures occupy important place in the processing of system design. Thus there are enormous applications of fuzzy information in the design of neural network classifiers.
\n
\n
Conflict of interest
I declare that I have no conflict of interest.
\n',keywords:"fuzzy set theory, entropy, fuzzy information measures, monotonicity, symmetry",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/62654.pdf",chapterXML:"https://mts.intechopen.com/source/xml/62654.xml",downloadPdfUrl:"/chapter/pdf-download/62654",previewPdfUrl:"/chapter/pdf-preview/62654",totalDownloads:952,totalViews:110,totalCrossrefCites:2,totalDimensionsCites:2,totalAltmetricsMentions:0,impactScore:1,impactScorePercentile:74,impactScoreQuartile:3,hasAltmetrics:0,dateSubmitted:"April 12th 2018",dateReviewed:"May 18th 2018",datePrePublished:null,datePublished:"October 31st 2018",dateFinished:"July 16th 2018",readingETA:"0",abstract:"Information theory deals with the study of problems concerning any system. This includes information processing, information storage, information retrieval and decision making. Information theory studies all theoretical problems connected with the transmission of information over communication channels. This includes the study of uncertainty (information) measures and various practical and economical methods of coding information for transmission. In this chapter, the introduction of a new generalised measure of fuzzy information involving two real parameters is given. The proposed measure satisfies all the necessary properties of being a measure. Some additional properties of the proposed measure have also been studied. Further, the monotonic nature of generalised fuzzy information measure with respect to the parameters is studied and validity of the same is checked by constructing the computed tables and plots on taking different fuzzy sets and different values of the parameters. Also, a new generalised fuzzy information measure involving three parameters has been introduced.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/62654",risUrl:"/chapter/ris/62654",book:{id:"6806",slug:"fuzzy-logic-based-in-optimization-methods-and-control-systems-and-its-applications"},signatures:"Anjali Munde",authors:[{id:"254393",title:"Dr.",name:"Anjali",middleName:null,surname:"Munde",fullName:"Anjali Munde",slug:"anjali-munde",email:"anjalidhiman2006@gmail.com",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",institution:null}],sections:[{id:"sec_1",title:"1. Background",level:"1"},{id:"sec_2",title:"2. Technical aspects of fuzzy measures",level:"1"},{id:"sec_3",title:"3. A new parametric measure of fuzzy information measure involving two parameters \n\nα\n\n and \n\nβ\n\n\n",level:"1"},{id:"sec_3_2",title:"3.1. Properties of \n\n\nH\nα\nβ\n\n\nA\n\n\n\n",level:"2"},{id:"sec_4_2",title:"3.2. Monotonic behaviour of fuzzy information measure",level:"2"},{id:"sec_6",title:"4. A new parametric measure of fuzzy information measure involving three parameters \n\nα\n\n, \n\nβ\n\n and \n\nγ\n\n\n",level:"1"},{id:"sec_6_2",title:"4.1. Properties of \n\n\nH\n\nα\n,\nβ\n,\nγ\n\n\n\nA\n\n\n\n",level:"2"},{id:"sec_7_2",title:"4.2. Monotonic behaviour of fuzzy information measure",level:"2"},{id:"sec_9",title:"5. Conclusions",level:"1"},{id:"sec_13",title:"Conflict of interest",level:"1"}],chapterReferences:[{id:"B1",body:'Shannon C. A mathematical theory of communication. Bell System Technical Journal. 1948;379–423:623-659\n'},{id:"B2",body:'Zadeh L. Fuzzy sets. Information and Control. 1966;8:94-102\n'},{id:"B3",body:'Renyi A. On measures of entropy and information. In: Proceedings of the 4th Berkeley Symposium on Mathematical Statistics and Probability; University of California Press; 1961. pp. 547-561\n'},{id:"B4",body:'Havrada J, Charvat F. Quantification methods of classification processes: Concept of structural α-entropy. Kybernetika. 1967;3:30-31\n'},{id:"B5",body:'Behara M, Chawla J. Generalized γ-entropy. Selecta Statistica Canadiana. 1974;2:15-38\n'},{id:"B6",body:'Kapur J. A comparative assessment of various measures of directed divergence. Advances in Management Studies. 1984;3:1-16\n'},{id:"B7",body:'Kapur J. Measures of Fuzzy Information. New Delhi: Mathematical Sciences Trust Society; 1997\n'},{id:"B8",body:'Kaufmann A. Fuzzy Subsets Fundamental Theoretical Elements. New York: Academic Press; 1980\n'},{id:"B9",body:'De Luca A, Termini S. A definition of a non-probabilistic entropy in setting of fuzzy sets. Information and Control. 1972;20:301-312\n'},{id:"B10",body:'Bhandari D, Pal N. Some new information measures for fuzzy sets. Information Sciences. 1993;67:209-228\n'},{id:"B11",body:'Sharma B, Taneja I. Entropies of type (α, β) and other generalized measures of information theory. Metrika. 1975;22:202-215\n'},{id:"B12",body:'Kapur J. Measures of Information and their Applications. New York: Wiley Eastern; 1995\n'},{id:"B13",body:'Kosko B. Fuzzy entropy and conditioning. Information Sciences. 1986;40:165-174\n'},{id:"B14",body:'Pal N, Pal S. Object background segmentation using new definition of entropy. IEEE Proceedings. 1989;136(A):284-295\n'},{id:"B15",body:'Prakash O, Gandhi C. New measures of information based upon measures of central tendency and dispersion. International Review of Pure and Applied Mathematics. 2008;4:161-172\n'},{id:"B16",body:'Prakash O, Gandhi C. New generalized measures of fuzzy entropy and their properties. Journal of Informatics and Mathematical Sciences. 2011;3:1-9\n'},{id:"B17",body:'Parkash O, Singh R. On characterization of useful information theoretic measures. Kybernetika. 1987;23:245-251\n'},{id:"B18",body:'Taneja I. On generalized information measures and their applications. Advances in Electronics and Electron Physics. 1989;76:327-413\n'},{id:"B19",body:'Taneja H, Tuteja R. Characterization of quantitative-qualitative measure of relative information. Information Sciences. 1984;33:217-222\n'},{id:"B20",body:'Tuteja R. On characterization of nonadditive measures of relative information and inaccuracy. Bulletin of the Calcutta Mathematical Society. 1983;77:363-369\n'},{id:"B21",body:'Tuteja R, Hooda D. On a generalized useful information measure of type α and degree β. Journal of the Indian Society of Statistics and Operations Research. 1985;6:1-11\n'},{id:"B22",body:'Tuteja R, Jain P. Characterization of relative useful information having utilities as monotone functions. Aplikace Matematiky. 1986;31:10-18\n'},{id:"B23",body:'Tuteja R, Jain P. An axiomatic characterization of relative useful information. Journal of Information and Optimization Sciences. 1986;7:49-57\n'},{id:"B24",body:'Tahayori H, Livi L, Sadeghian A, Rizzi A. Interval type-2 fuzzy set reconstruction based on fuzzy information-theoretic kernels. IEEE Transactions on Fuzzy Systems. 2015;23(4):1014-1029\n'},{id:"B25",body:'Kumar T, Bajaj R. NTV metric based entropies of interval-valued intuitionistic fuzzy sets and their applications in decision making. Ann. Fuzzy Math. Inform. 2015;9(1):1-21\n'},{id:"B26",body:'Mishra A, Hooda D, Jain D. On exponential fuzzy measures of information and discrimination. International Journal of Computer Applications. 2015;119(23):1-7\n'},{id:"B27",body:'Hooda D, Mishra A. On trigonometric fuzzy information measures. ARPN Journal of Science and Technology. 2015;5(3):145-152\n'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Anjali Munde",address:"anjalidhiman2006@gmail.com",affiliation:'
Amity University, Uttar Pradesh, India
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Polyps",doi:"10.5772/intechopen.90327",slug:"reahs-and-reah-like-lesions-underdiagnosed-lesions-often-misconfused-with-nasal-polyps",body:'
1. Introduction
REAH is the eponysm for Respiratory Epithelial Adenomatoid Hamartoma. It is a relatively new diagnosis, only added to the World Health Organization classification of tumors in 2005 [1].
Wenig and Heffner were the first to describe it in 1995 in a series of 31 cases [2]. They described it as “a proliferation of glands lined by multi-layered ciliated respiratory epithelium, often with admixed mucocytes, arising in direct continuity with the surface epithelium, which invaginated downward into the submucosa.”
The lesion is usually diagnosed in middle-aged patients. Clinically it may manifest as a solitary lesion or in association with sinonasal polyposis. The former is far less common than the latter. The lesion takes its origin either in the olfactory cleft, the posterior septum, or the rhinopharynx [1, 2, 3, 4, 5] Because the incidence, clinical signs, imaging, modality of treatment, outcomes, and pathogenesis seem to be quiet different between these two clinical patterns, we call the first ones “REAHs” and the second ones “REAH-like.” This terminology is proposed by Jankowski [3, 5] and Hawley [4] as well.
The purpose of this paper is to remind the histopathological characteristics and differential diagnosis of REAHs/REAH-like lesions and to report two different cohorts of patients (one with REAHs and the other with REAH like lesions), treated in the ENT department of the CHU UCL Namur.
2. Histopathological characteristics of REAHs and REAH-like lesions
Grossly, REAH looks like a “polypoid fleshy to firm mass with areas of induration.” It is yellow or white [6]. It may have varying sizes (Figures 1–3).
Figure 1.
Gross appearance of a REAH.
Figure 2.
REAHs: The glandular proliferation arises in direct continuity with the surface epithelium with invagination downward into the submucosa. Clusters of seromucinous glands are seen.
Figure 3.
REAHs: Occasionally the gland lumina are filled with mucinous or eosinophilic amorphous material. It often demonstrates periglandular stromal hyalinization, and there is often a mixed inflammatory infiltrate within the stroma.
The histologic picture is dominated by the presence of a glandular proliferation with a polypoid appearance. The proliferation starts from the surface epithelium and tends to be submucosal.
The glands are lined by ciliated respiratory epithelium originating from the surface respiratory epithelium. The glands are typically round to oval in shape and were small to medium in size with prominent dilation. Stromal tissue separates the glands. The epithelium may be cuboidal or flat, and mucinous gland metaplasia is often seen. Occasionally the gland lumina are filled with mucinous or eosinophilic amorphous material. It often demonstrates periglandular stromal hyalinization, and there is often a mixed inflammatory infiltrate within the stroma.
In the literature we can find another type of REAH called COREAH. It is characterized by a chondro-osseous differentiation. Flavin [7] and Roffman [8] were the two first authors to publish this entity, respectively, in 2005 and 2006. Since then 11 cases have been reported [9, 10]. It can occur in children or adults.
The histological features are almost exactly the same as REAH, but COREAH has islands of immature hyaline cartilage interspersed throughout the lesion (Figures 4 and 5).
Figure 4.
COREAH: Nasal chondromesenchymal hamartoma. Multiple tumor fragments with a mucosal surface and nodules of cartilage (in red).
Figure 5.
Seromucinous hamartoma: The mass is covered by respiratory epithelium and is comprised of lobular or haphazard proliferations of small to large glands and ducts which are lined by a single layer of cuboidal or flattened epithelial cells.
3. Immunohistochemistry of REAHs
Immunohistochemistry has not been used to an extensive degree in the diagnosis of REAH, and it is not absolutely necessary to use it to make the definitive diagnosis of it.
However, Ozolek et al. did an immunohistochemical study in which they examined the profile of REAH [11]. REAHs are positive for CK7, negative for CK20 and CDX-2, and positive for MIB1 and Ki67. p63 staining was seen in the basal cells of REAH, which had a low proliferation index. The use of Mindbomb 1 (MIB-1) is useful in distinguishing REAH from other neoplasms, since neoplasms tend to have a high proliferation index.
REAHs: Immunohistochemistry: Positivity for CK7 and negativity for CK20.
4. Differential diagnosis of REAHs
The differential diagnostic of REAHs concerns the inflammatory polyps, Schneiderian papillomas, seromucinous hamartoma, and low-grade non-intestinal adenocarcinoma.
4.1 Inflammatory polyps
Inflammatory polyps are certainly the most common lesions that are confused with REAHs.
The most notable clinical differences between REAHs and inflammatory polyps are the location and their gross appearance.
Inflammatory polyps are typically the clinical manifestation of a sinonasal polyposis. Nasal polyps are rarely isolated. They are multiple and bilateral and usually extrude from the middle and superior meati. They are rarely attached to the posterior septum. REAHs originate specifically from the olfactory cleft.
Nasal polyps are usually edematous and not indurated. On microscopy, both lesions can show fibroblastic and vascular proliferation, stromal edema, a mixed inflammatory cell infiltrate, and seromucinous gland proliferation. However, inflammatory polyps do not have florid adenomatoid proliferation and stromal hyalinization which, when present, favor REAHs (Figures 6–9).
Figure 6.
Macroscopic and endoscopic view of a nasal polyp.
Figure 7.
Endoscopic view: right and left nasal cavity: presence of nasal polyps in the middle and superior meati.
Figure 8.
Inflammatory polyp with edematous inflammatory stroma and single-layered glands.
Figure 9.
Inflammatory polyp showing inflammatory stroma without hyalinization.
4.2 Schneiderian papillomas
This is the second important differential diagnosis of REAHs.
Schneiderian papillomas are benign epithelial neoplasms of the sinonasal tract. Their annual incidence ranges between 0.2 and 1.5/100,000 people per year.
They are classified in three types: exophytic/fungiform papilloma, endophytic/inverted papilloma, and oncocytic/cylindrical cell papilloma. The inverted type is the most common, accounting for nearly two thirds of the cases. We limit the description to this type.
It is mostly unilateral. It occurs mainly in adults during the fifth or sixth decade. There is a predilection for men.
Unlike inflammatory polyps and REAHs, inverted papillomas are considered true neoplasms. While REAHs tend to be located medial to the turbinate lamella, inverted papillomas have a predilection for the lateral wall of the nasal cavity or the paranasal cavities. Maxillary and ethmoid sinuses are the most common origins followed by the sphenoid and frontal sinuses. Even if inverted papillomas are benign histologic lesions, clinically they may be aggressive with a relatively strong potential for local destruction, high rate of recurrence (more or less 50%), and a risk of carcinomatous evolution. This transformation in squamous cell carcinoma can be synchrone or metachrone and more likely in case of recurrence. This malignant transformation has never been observed in the case of REAHs.
Human papilloma virus seems to be implicated in the pathogenesis of inverted papillomas. Chronic inflammation seems to be a favorizing factor in REAHs.
The treatment of inverted papilloma requires a more extensive and radical excision with a subperiosteal dissection and a drilling of the base of implantation. Endonasal medial maxillectomy is the golden standard for maxillary sinus origin. Recurrence is more likely in frontal sinus papillomatosis due to the localization and the difficulty to completely eradicate the lesion. The surgical treatment for REAHs is a complete excision without ethmoidectomy.
Grossly, inverted papilloma looks like a reddish-gray lobulated tumor, more firm than an inflammatory polyp, with a fairly characteristic “raspberry” aspect (Figure 10).
Figure 10.
Endoscopic view of an inverted papilloma originating from the left maxillary sinus.
Histologically inverted papillomas have an endophytic growth pattern. There is an invagination of stratified squamous epithelium with an admixture of mucin containing cells and microcysts. The epithelium may be of squamous, transitional, or respiratory type. The endophytic growth of squamous epithelium is not seen in REAH. Transmigrating neutrophils and neutrophilic microabscesses may be seen. Occasional mitoses may be seen in the basal layer. Mild to moderate atypia may be seen. Edema or chronic inflammatory infiltrate is present in the stroma (Figures 11–13).
Figure 11.
Low magnification: typical view of an IP: it shows an endophytic growth pattern consisting of markedly thickened squamous epithelial proliferation growing downward into the underlying connective tissue stroma to form large clefts, ribbons, and islands. Note the absence of mucoserous glands. Delicate basement membrane.
Figure 12.
Immunohistochemistry: high power shows the epithelium to be composed of pseudostratified columnar cells/positivity of MIB1 in the basal cells.
Figure 13.
Immunohistochemistry: high power/positivity of CK7.
4.3 Seromucinous hamartoma
Seromucinous hamartoma is another subtype of hamartoma, recently described. It is a benign lesion of the sinonasal tract as well, located in the posterior nasal cavity or rhinopharynx frequently associated to REAHs. Since its description in 1974 [12], only a small number of additional cases have been reported.
The lesion occurs equally in men and women. Patients are middle-aged to elderly (mean age 50–60) and have complaints with nasal obstruction or nosebleeds. Surgical excision is the treatment of choice. It is included in the differential diagnosis of low grade epithelial proliferations of the sinonasal tract. The differentiation with low-grade non-intestinal adenocarcinoma can be tricky.
Histologically, the mass looks like a benign lesion. Lobular or haphazard proliferations of small to large glands and ducts lined by a single layer of cuboidal or flattened epithelial cells are visualized. Eosinophilic secretions are often present within tubules. The surrounding stroma often contains a lymphoplasmocytic inflammatory infiltrate. Periglandular hyalinization can be observed. There are no features suggesting a malignancy. There are no nuclear atypia.
Seromucinous hamartomas are positive for CK7 and CK19 and negative for CK14 and CK20. The serous glands are usually S100 positive and negative for p63 and muscle-specific antigen.
4.4 Low-grade sinonasal adenocarcinoma (LGSNAC)
Sinonasal adenocarcinoma is the third differential diagnosis for REAH. It accounts for approximately 20% of all sinonasal malignancies and is classified into intestinal and non-intestinal salivary and non-salivary types. Intestinal adenocarcinomas (also called ITAC) take their origin in the olfactory cleftl and then extend into the ethmoid sinus, the orbit, or the anterior cranial fossa. It is an occupational disease; they typically occur in woodworkers. They look like an irregular exophytic pink necrotic and friable mass bulging into the nasal cavity located between the nasal septum and the turbinate lamella.
On microscopy, papillary and colonic types are the most common architectures. Differentiating ITAC from REAH is usually not difficult as the cell types, high-grade features, and increased mitotic index are characteristics for ITAC. ITAC is positive for CK20 and MIB1 and negative for CK7 (Figure 14).
Figure 14.
Intestinal-type adenocarcinoma: Immunohistochemistry—Positivity for CK20, CK7, and MIB1.
On the other hand, low-grade non-intestinal adenocarcinomas (LGSNAC) are less common and less invasive. There is no sex or racial predilection. There is no association with wood dust exposure. They have no tendency to give systemic metastasis. However, they have a potential for local invasion and destruction of tissue. Extensive surgery is recommended to be associated with radiotherapy in some cases.
Histologically, the mass originates from the surface epithelium and the seromucinous glands of the submucosa. It consists of glandular proliferations lined by cuboidal to columnar cells which are usually monomorphic and cytologically bland. It forms a diverse group of bland tubular and/or papillary tumors. Mitoses are rare. Necrosis, perineural invasion, and lymphovascular invasion are absent. The stroma contains an inflammatory infiltrate as in REAHs.
Immunohistochemistry shows the positivity for CK7 and S100 and negativity for CK20 and CDX2.
The main differential diagnosis is between LGSNAC and seromucinous hamartoma (Figure 15).
Figure 15.
LGSNAC: Glandular proliferations lined by cuboidal to columnar cells which are usually monomorphic and cytologically bland.
5. Our experience
5.1 REAHs as a solitary lesion
This clinical presentation of REAHs is actually the less frequent.
Table 1 reports a cohort of eight cases diagnosed and treated in the ENT department of the CHU UCL Namur since 2008.
There were seven women. The mean age was 65 years old. Ranges are 27 and 81.
There was one man: age 53 years old.
The lesions were unilateral in six patients (three left sided; three right sided) and bilateral in two.
Two patients were asymptomatic. REAH was diagnosed by nasal endoscopy and a sinus CT scanner performed for an assessment of epiphora, a case of nasal dysfunction and another one to rule out sinus disease associated to his allergic rhinitis.
The other patients complained with nasal obstruction and rhinorrhea.
REAHS originated from the olfactory cleft in six patients and from the anterior wall of the sphenoid sinus in two cases.
On nasal endoscopy the lesion looked fleshy, with no vascular component and no necrosis.
On imaging the lesion was solitary in the olfactory cleft. No chronic rhinosinusitis was present (Figure 16).
Figure 16.
Comparison between CT scan and nasal endoscopy.
The MRI performed in three cases was not so helpful. There were no pathognomonic features whatever was the localization. In the literature, REAHs appear as a homogeneous mass with post-contrast enhancement on T1-weighted sequences as well as hyperintensity on T2-weighted images (Figure 17) [13].
Figure 17.
MRI of a patient with bilateral REAHs: T1- and T2-weighted sequences.
The diagnosis of REAH was confirmed in all the cases by the pathologist.
In one case it was a COREAH, and in another case it was a seromucinous hamartoma. These two hamartomas were located in the posterior nasal fossa.
A biopsy was performed under local anesthesia in asymptomatic cases to make a formal diagnosis. For the other the diagnosis was made on the surgical specimen.
There was no clear etiologic factor that could have played a role in the development of REAH except in one patient suffering from allergic rhinitis. There was no concomitant chronic sinusitis, asthma, or aspirin intolerance.
Concerning the management, in two patients a wait and see attitude was proposed as the patient was not symptomatic. For the others an endoscopic resection of the lesion was performed under general anesthesia. The dissection was done in a subperiosteal plane. We have never drilled out the site of implantation. There was no need to do a full house ethmoidectomy.
Primary severe nasal polyposis: no asthma: operated in 2013/REAHs
Tri. Fr.
M
Ethmoidectomy 10 y ago/nasal polyposis/ REAHs
V. Mo
F
Nasal polyposis /asthma/previous FESS/REAHs X2
Table 2.
Cohort of patients with REAH-like lesions.
5.2.1 Epidemiology
The series includes 13 men and 2 women. The mean average is about 63 years old.
The majority of the patients are in the fifth and sixth decades.
All the patients suffer from a nasal polyposis. In two cases it was a massive primary polyposis. The other patients have a nasal polyposis operated in the past. The REAHs were diagnosed at the revision surgery.
Eight patients have concomitant asthma. Two patients have aspirin intolerance.
Two patients have allergic rhinitis.
Chronic inflammation plays a role in the development of REAHs in this clinical pattern.
5.2.2 Nasal endoscopy
REAHs are located in the olfactory cleft. Their macroscopic aspect is different than usual nasal polyps extruding from the ethmoid sinus. They are more fleshy and firm. There is no necrosis.
As the following pictures show, it is extremely difficult to differentiate with the fibroscopy REAHs and inflammatory polyps in case of recurrent nasal polyposis. The histologic examination of the surgical specimens is mandatory for this differentiation (Figure 19).
Figure 19.
Comparison of the nasal endoscopy and the histological pattern. The inflammation in the stroma is much more important than in pure REAHs.
5.2.3 Imaging
CT imaging findings are described in only a limited number of studies [1, 4, 5, 14]. Lima et al. [5], Hawley et al. [4], and Lee et al. (51 cases) [14] conclude that REAHs cause widening of the olfactory cleft more than 10 mm but generally do not cause bone erosion.
All the paranasal sinus cavities can be opaque as illustrated by the following pictures (Figures 20–22):
Figure 20.
CT showing a severe nasal polyposis; widening of the olfactory cleft raises suspicion of REAHs.
Figure 21.
Patient with REAHs in the olfactory cleft. She had a standard ethmoidectomy for nasal polyposis. We observe REAHs in the olfactory cleft. Correlation between CT scan and nasal endoscopy.
Figure 22.
Typical CT scan showing the opacity of both olfactory clefts caused by REAHs.
Some patients have a long-standing disease; REAHs develop after the surgery with time. Some of them are attached to the anterior and superior portion of the nasal septum and cause blockage of the frontal sinus pathway or even thinning and erosion of the nasal bones.
Same patient with thinning and erosion of the nasal bones (arrows) and opacity of both frontal sinuses.
MRI can be of some help to rule out other lesions such as encephalocele, olfactory neuroblastoma, or glioma.
The management of REAHs associated with nasal polyposis must be discussed case by case.
A complete sphenoethmoidectomy is usually necessary to manage the recurrent nasal polyposis.
For the REAHs, debulking or better exenteration of the olfactory cleft must be considered. But we know that it can be tricky and risky for the skull base with a risk of CSF leak if the surgery is too aggressive. Resection of the REAHs is usually more bloody than during a polypectomy.
In the case of frontal opacity caused by REAHs attached to the anterior and superior septa, a Draf III procedure must be considered.
After surgery medical treatment of the nasal polyposis and asthma remains absolutely necessary to prevent or delay as much as possible recurrences.
6. Conclusion
REAHs and REAH-like lesions are relatively new clinical entities. Despite numerous publications they are still underdiagnosed. These lesions are located in the olfactory clefts. They can be isolated or in association with nasal polyposis typically in the case of recurrence after FESS.
The clinicians and pathologists must know these lesions. They are usually benign, but in some cases they are associated to frontal sinus blockage and widening of the nasal vault; loss of smell is common. The differential diagnosis includes diseases with more severe morbidities such as inverted papilloma, seromucinous hamartomas, and low-grade non-intestinal adenocarcinoma.
Histological examination of all the surgical specimens is necessary.
The treatment is dictated by the disease.
The extent of the surgery depends on the type and size of the REAHs and the associated disease.
It consists of a limited polypectomy or a complete exenteration of the olfactory cleft associated or not to a full house ethmoidectomy and even a Draf III procedure.
\n',keywords:"REAHs, REAH-like, nasal polyposis, olfactory cleft",chapterPDFUrl:"https://cdn.intechopen.com/pdfs/70344.pdf",chapterXML:"https://mts.intechopen.com/source/xml/70344.xml",downloadPdfUrl:"/chapter/pdf-download/70344",previewPdfUrl:"/chapter/pdf-preview/70344",totalDownloads:893,totalViews:0,totalCrossrefCites:0,dateSubmitted:"June 19th 2019",dateReviewed:"October 30th 2019",datePrePublished:"December 4th 2019",datePublished:"October 21st 2020",dateFinished:"December 4th 2019",readingETA:"0",abstract:"REAH is the eponym for respiratory epithelial adenomatoid hamartoma. The disease is under diagnosed. It is clearly a disease in the olfactory cleft. It is characterized by a polypoid process located in the olfactory cleft which does not evolve in inverted papilloma or malignancy set at 10–15 cm. The lesion can be isolated in one or both olfactory cleft. It can be asymptomatic or can cause nasal obstruction and impairment of smell. More commonly the lesions, often multiple, are associated to the recurrence of the nasal polyposis. They can contribute to the development of loss of smell, nasal obstruction or even the blockage of the frontal recesses. The definitive diagnostic is based upon the histologic examination. Surgery is the treatment. In case of isolated lesion, complete excision without complete ethmoidectomy is the option. In case of lesions embedded in a recurrent massive polyposis, a complete exenteration of the olfactory clefts associated to a revision of full house ethmoidectomy and even a Draf III must be considered.",reviewType:"peer-reviewed",bibtexUrl:"/chapter/bibtex/70344",risUrl:"/chapter/ris/70344",signatures:"Ph. Eloy, C. Fervaille and M.C. Nollevaux",book:{id:"8732",type:"book",title:"Sino-Nasal and Olfactory System Disorders",subtitle:null,fullTitle:"Sino-Nasal and Olfactory System Disorders",slug:"sino-nasal-and-olfactory-system-disorders",publishedDate:"October 21st 2020",bookSignature:"Thomas Heinbockel and Balwant Singh Gendeh",coverURL:"https://cdn.intechopen.com/books/images_new/8732.jpg",licenceType:"CC BY 3.0",editedByType:"Edited by",isbn:"978-1-83880-951-5",printIsbn:"978-1-83880-950-8",pdfIsbn:"978-1-83880-952-2",isAvailableForWebshopOrdering:!0,editors:[{id:"70569",title:"Dr.",name:"Thomas",middleName:null,surname:"Heinbockel",slug:"thomas-heinbockel",fullName:"Thomas Heinbockel"}],productType:{id:"1",title:"Edited Volume",chapterContentType:"chapter",authoredCaption:"Edited by"}},authors:[{id:"308649",title:"Prof.",name:"Philippe",middleName:null,surname:"Eloy",fullName:"Philippe Eloy",slug:"philippe-eloy",email:"philippe.eloy@uclouvain.be",position:null,profilePictureURL:"//cdnintech.com/web/frontend/www/assets/author.svg",institution:null}],sections:[{id:"sec_1",title:"1. Introduction",level:"1"},{id:"sec_2",title:"2. Histopathological characteristics of REAHs and REAH-like lesions",level:"1"},{id:"sec_3",title:"3. Immunohistochemistry of REAHs",level:"1"},{id:"sec_4",title:"4. Differential diagnosis of REAHs",level:"1"},{id:"sec_4_2",title:"4.1 Inflammatory polyps",level:"2"},{id:"sec_5_2",title:"4.2 Schneiderian papillomas",level:"2"},{id:"sec_6_2",title:"4.3 Seromucinous hamartoma",level:"2"},{id:"sec_7_2",title:"4.4 Low-grade sinonasal adenocarcinoma (LGSNAC)",level:"2"},{id:"sec_9",title:"5. Our experience",level:"1"},{id:"sec_9_2",title:"5.1 REAHs as a solitary lesion",level:"2"},{id:"sec_10_2",title:"5.2 REAHs associated to a nasal polyposis often previously operated also called REAH-like lesions",level:"2"},{id:"sec_10_3",title:"5.2.1 Epidemiology",level:"3"},{id:"sec_11_3",title:"5.2.2 Nasal endoscopy",level:"3"},{id:"sec_12_3",title:"5.2.3 Imaging",level:"3"},{id:"sec_15",title:"6. Conclusion",level:"1"}],chapterReferences:[{id:"B1",body:'VandenBossche S, De Vos G, Lemmerling MA. Typical but underdiagnosed nasal cavity Mass. Journal of the Belgian Society of Radiology. 2018;102(1):35'},{id:"B2",body:'Wenig BM, Heffner DK. Respiratory epithelial adenomatoid hamartomas of the sinonasal tract and nasopharynx: A clinicopathologic study of 31 cases. Annals of Otology, Rhinology, and Laryngology. 1995;104(8):639-645'},{id:"B3",body:'Nguyen DT, Gauchotte G, Arous F, Vignaud J-M, Jankowski R. Respiratory epithelial adenomatoid hamartoma of the nose: An updated review. American Journal of Rhinology & Allergy. 2014;28(5):187-192'},{id:"B4",body:'Hawley KA, Ahmed M, Sindwani R. CT findings of sinonasal respiratory epithelial adenomatoid hamartoma: A closer look at the olfactory clefts. American Journal of Neuroradiology. 2013;34(5):1086-1090'},{id:"B5",body:'Lima NB, Jankowski R, Georgel T, Grignon B, Guillemin F, Vignaud J-M. Respiratory adenomatoid hamartoma must be suspected on CT-scan enlargement of the olfactory clefts. Rhinology. 2006;44(4):264-269'},{id:"B6",body:'Bullock MJ. Low-grade epithelial proliferations of the sinonasal tract. Head and Neck Pathology. 2016;10(1):47-59'},{id:"B7",body:'Flavin R, Russell J, Phelan E, McDermott MB. Chondroosseous respiratory epithelial adenomatoid hamartoma of the nasal cavity: A case report. International Journal of Pediatric Otorhinolaryngology. 2005;69:87-91'},{id:"B8",body:'Roffman E, Baredes S, Mirani N. Respiratory epithelial adenomatoid hamartomas and chondro-osseous respiratory epithelial adenomatoid hamartomas of the sinonasal tract: A case series and literature review. American Journal of Rhinology. 2006;20:596-590'},{id:"B9",body:'Daniel A, Wong E, Ho J, Singh N. Chondro-osseous respiratory epithelial adenomatoid hamartoma (COREAH): Case report and literature review. Case Reports in Otolaryngology. 2019;2019. Article ID 5247091. 4p'},{id:"B10",body:'Ozolek JA, Barnes EL, Hunt JL. Basal/myoepithelial cells in chronic sinusitis, respiratory epithelial adenomatoid hamartoma, inverted papilloma, and intestinal-type and nonintestinal-type sinonasal adenocarcinoma: An immunohistochemical study. Archives of Pathology & Laboratory Medicine. 2007;131:530-537'},{id:"B11",body:'Ozolek JA, Barnes EL, Hunt JL. Basal/myoepithelial cells in chronic sinusitis, respiratory epithelial adenomatoidhamartoma, inverted papilloma, and intestinal-type and nonintestinal-type sinonasal adenocarcinoma: An immunohistochemical study. Archives of Pathology & Laboratory Medicine. 2007;131:530-537'},{id:"B12",body:'Baillie EE, Batsakis JG. Glandular (seromucinous) hamartoma of the nasopharynx. Oral Surgery, Oral Medicine, and Oral Pathology. 1974;38:760-762'},{id:"B13",body:'Braun J-J, Riehm S, Averous G, Billing A, Veillon F. MRI in respiratory epithelial adenomatoidhamartoma of nasal cavities. Journal of Neuroradiology. 2013;40(3):216-219'},{id:"B14",body:'Lee JT, Garg R, Brunworth J, Keschner DB, Thompson LDR. Sinonasal respiratory epithelial adenomatoid hamartomas: Series of 51 cases and literature review. American Journal of Rhinology & Allergy. 2013;27(4):322-328'}],footnotes:[],contributors:[{corresp:"yes",contributorFullName:"Ph. Eloy",address:"philippe.eloy@uclouvain.be",affiliation:'
ENT Department, CHU UCL Namur, Site of Godinne, Belgium
Department of Pathology, CHU UCL Namur, Site of Godinne, Belgium
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Saleh and Amal I. Hassan",coverURL:"https://cdn.intechopen.com/books/images_new/11120.jpg",editedByType:"Edited by",publishedDate:"June 23rd 2022",editors:[{id:"144691",title:"Prof.",name:"Hosam M.",middleName:null,surname:"Saleh",slug:"hosam-m.-saleh",fullName:"Hosam M. Saleh"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"10696",title:"Applications of Calorimetry",subtitle:null,isOpenForSubmission:!1,hash:"8c87f7e2199db33b5dd7181f56973a97",slug:"applications-of-calorimetry",bookSignature:"José Luis Rivera Armenta and Cynthia Graciela Flores Hernández",coverURL:"https://cdn.intechopen.com/books/images_new/10696.jpg",editedByType:"Edited by",publishedDate:"June 23rd 2022",editors:[{id:"107855",title:"Dr.",name:"Jose Luis",middleName:null,surname:"Rivera Armenta",slug:"jose-luis-rivera-armenta",fullName:"Jose Luis Rivera Armenta"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}]},subject:{topic:{id:"372",title:"Phytology",slug:"phytology",parent:{id:"41",title:"Plant Biology",slug:"agricultural-and-biological-sciences-plant-biology"},numberOfBooks:4,numberOfSeries:0,numberOfAuthorsAndEditors:81,numberOfWosCitations:135,numberOfCrossrefCitations:18,numberOfDimensionsCitations:35,videoUrl:null,fallbackUrl:null,description:null},booksByTopicFilter:{topicId:"372",sort:"-publishedDate",limit:12,offset:0},booksByTopicCollection:[{type:"book",id:"9704",title:"Cucumber Economic Values and Its Cultivation and Breeding",subtitle:null,isOpenForSubmission:!1,hash:"779dad6540f8023acf09657acf0b5da8",slug:"cucumber-economic-values-and-its-cultivation-and-breeding",bookSignature:"Haiping Wang",coverURL:"https://cdn.intechopen.com/books/images_new/9704.jpg",editedByType:"Edited by",editors:[{id:"280406",title:"Dr.",name:"Haiping",middleName:null,surname:"Wang",slug:"haiping-wang",fullName:"Haiping Wang"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"8044",title:"Root Biology",subtitle:"Growth, Physiology, and Functions",isOpenForSubmission:!1,hash:"e29d230e2fb39fddbf72452c91fe411d",slug:"root-biology-growth-physiology-and-functions",bookSignature:"Takuji Ohyama",coverURL:"https://cdn.intechopen.com/books/images_new/8044.jpg",editedByType:"Edited by",editors:[{id:"30061",title:"Prof.",name:"Takuji",middleName:null,surname:"Ohyama",slug:"takuji-ohyama",fullName:"Takuji Ohyama"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"7491",title:"Forage Groups",subtitle:null,isOpenForSubmission:!1,hash:"0f0fb28490411c41af2c39eaf6412aec",slug:"forage-groups",bookSignature:"Ricardo Loiola Edvan and Edson Mauro Santos",coverURL:"https://cdn.intechopen.com/books/images_new/7491.jpg",editedByType:"Edited by",editors:[{id:"283266",title:"Dr.",name:"Ricardo",middleName:null,surname:"Loiola Edvan",slug:"ricardo-loiola-edvan",fullName:"Ricardo Loiola Edvan"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}},{type:"book",id:"1814",title:"Botany",subtitle:null,isOpenForSubmission:!1,hash:"c692bbecba40bcdc059399e3ddb10de2",slug:"botany",bookSignature:"John Kiogora Mworia",coverURL:"https://cdn.intechopen.com/books/images_new/1814.jpg",editedByType:"Edited by",editors:[{id:"26063",title:"Dr.",name:"John",middleName:"Kiogora",surname:"Mworia",slug:"john-mworia",fullName:"John Mworia"}],equalEditorOne:null,equalEditorTwo:null,equalEditorThree:null,productType:{id:"1",chapterContentType:"chapter",authoredCaption:"Edited by"}}],booksByTopicTotal:4,seriesByTopicCollection:[],seriesByTopicTotal:0,mostCitedChapters:[{id:"67771",doi:"10.5772/intechopen.87083",title:"The Role of Plant Growth-Promoting Bacteria in the Growth of Cereals under Abiotic Stresses",slug:"the-role-of-plant-growth-promoting-bacteria-in-the-growth-of-cereals-under-abiotic-stresses",totalDownloads:1607,totalCrossrefCites:7,totalDimensionsCites:13,abstract:"Plant growth-promoting rhizobacteria (PGPR) are known to improve plant performance by multiple mechanisms, such as the production of beneficial hormones, the enhancement of plant nutritional status, and the reduction of the stress-related damage. The interaction between plants and PGPR becomes of particular interest in environments that are characterized by suboptimal growing conditions, e.g., high or low temperatures, drought, soil salinity, and nutrient scarcity. The positive role of PGPR will become even more appealing in the future, as world agriculture is facing issues as climate change and soil degradation. This chapter aims to discuss the main mechanisms of the interaction between PGPR and plants and will focus of how PGPR can decrease abiotic stress damage in cereals, which are critical crops for human diet.",book:{id:"8044",slug:"root-biology-growth-physiology-and-functions",title:"Root Biology",fullTitle:"Root Biology - Growth, Physiology, and Functions"},signatures:"Martino Schillaci, Sneha Gupta, Robert Walker and Ute Roessner",authors:null},{id:"64176",doi:"10.5772/intechopen.81186",title:"Tropical Forage Legumes in India: Status and Scope for Sustaining Livestock Production",slug:"tropical-forage-legumes-in-india-status-and-scope-for-sustaining-livestock-production",totalDownloads:2010,totalCrossrefCites:3,totalDimensionsCites:6,abstract:"Livestock contributes enormously in food and nutritional security apart from livelihood security to rural population all over the world. India has the largest number of livestock, representing over 17% of world population. Availability of forage legumes is essential for better animal health, production and increasing the nutritive value of forage-based rations, besides providing a source of biological nitrogen fixation for enriching soil, reducing land degradation and mitigating climate change. However, supply of quality green fodder in India is extremely precarious, and the gap is huge against demand. The major fodder legume crops cultivated in India are Medicago sativa, Trifolium alexandrinum, Vigna unguiculata, Vigna umbellate and range legumes are Stylosanthes spp., Desmanthus virgatus, and Clitoria ternatea. Indian subcontinent represents wide spectrum of eco-climates and reported diversity of 21 forage legumes genera viz., Desmodium, Lablab, Stylosanthes, Vigna, Macroptelium, Centrosema and browse plants Leucaena, Sesbania, Albizia, Bauhinia, Cassia, Grewia, etc. Diversity of forage legumes were collected (>3200 accessions), evaluated and sources for different biotic and abiotic stress tolerance were identified, apart from >50 cultivars developed. Considering these aspects, tropical legumes for livestock production, soil health and ecosystem services, diversity, evaluation and breeding for improved varieties are discussed in this chapter.",book:{id:"7491",slug:"forage-groups",title:"Forage Groups",fullTitle:"Forage Groups"},signatures:"Tejveer Singh, Srinivasan Ramakrishnan, Sanat Kumar Mahanta,\nVikas C. Tyagi and Ajoy Kumar Roy",authors:[{id:"254954",title:"Dr.",name:"Srinivasan",middleName:null,surname:"Ramakrishnan",slug:"srinivasan-ramakrishnan",fullName:"Srinivasan Ramakrishnan"},{id:"254958",title:"Dr.",name:"Tejveer",middleName:null,surname:"Singh",slug:"tejveer-singh",fullName:"Tejveer Singh"},{id:"254959",title:"Dr.",name:"Sanath Kumar",middleName:null,surname:"Mahanta",slug:"sanath-kumar-mahanta",fullName:"Sanath Kumar Mahanta"},{id:"254960",title:"Dr.",name:"Vikas",middleName:null,surname:"Tyagi",slug:"vikas-tyagi",fullName:"Vikas Tyagi"},{id:"254961",title:"Dr.",name:"A.K.",middleName:null,surname:"Roy",slug:"a.k.-roy",fullName:"A.K. Roy"}]},{id:"65365",doi:"10.5772/intechopen.83402",title:"Mob Grazing Results in High Forage Utilization and Reduced Western Snowberry Size",slug:"mob-grazing-results-in-high-forage-utilization-and-reduced-western-snowberry-size",totalDownloads:966,totalCrossrefCites:0,totalDimensionsCites:3,abstract:"Mob-grazing strives to maximize forage utilization and minimize selective grazing by using high stocking densities in small paddocks for short durations (12–24 hr). Rotational-grazing uses low stocking densities for a longer time period, retaining about half of the original available forage; although selective grazing can occur. Three cattle (Bos taurus × Bos indicus) grazing intensities: mob- (stocking densities from 32,000 to 67,000 kg ha−1; duration—24 hr); rotation (stocking density—2500 kg ha−1; duration—35 d); and non-grazed systems were compared based on forage utilization and changes to western snowberry (Symphoricarpos occidentalis) (WS) patch volume in a 2-year South Dakota study. Pre- and post-grazing forage height was measured every 2.5 m along multiple 50-m transects with WS patch volume measured every 5 m. Forage utilization (consumed and trampled) ranged from 42 to 90% in mob-grazed areas, and harvest efficiency (forage consumed) ranged from 15 to 64%. WS patch volumes decreased by ≥45% in mob-grazed treatments compared with no change in rotational-grazing and increased cover in non-grazed areas. WS pre-graze patch size influenced mob-grazing impact; patches >6500 cm3 were browsed or trampled to a greater extent than smaller patches.",book:{id:"7491",slug:"forage-groups",title:"Forage Groups",fullTitle:"Forage Groups"},signatures:"Heidi Reed, Sharon Clay, Alexander Smart, David Clay and Michelle\nOhrtman",authors:[{id:"37140",title:"Prof.",name:"David",middleName:null,surname:"Clay",slug:"david-clay",fullName:"David Clay"},{id:"87430",title:"Prof.",name:"Sharon",middleName:null,surname:"Clay",slug:"sharon-clay",fullName:"Sharon Clay"},{id:"255998",title:"Dr.",name:"Heidi",middleName:null,surname:"Reed",slug:"heidi-reed",fullName:"Heidi Reed"},{id:"256000",title:"Dr.",name:"Alexander",middleName:null,surname:"Smart",slug:"alexander-smart",fullName:"Alexander Smart"},{id:"285225",title:"Dr.",name:"Michelle",middleName:null,surname:"Ohrtman",slug:"michelle-ohrtman",fullName:"Michelle Ohrtman"}]},{id:"68685",doi:"10.5772/intechopen.87099",title:"Morphological and Physiological Root Plasticity and Its Relationships with Shoot Growth of Rice with Water Regimes and Microbial Densities",slug:"morphological-and-physiological-root-plasticity-and-its-relationships-with-shoot-growth-of-rice-with",totalDownloads:847,totalCrossrefCites:1,totalDimensionsCites:2,abstract:"There is renewed interest in root research for undergirding a second Green Revolution. The modular nature of root systems makes them amenable to both morphological and/or physiological plasticity when encountering heterogeneous environments. Such plasticity, the ability to change and adapt in response to variations in the underground environment, is linked to a shoot response and to consequent dry matter production, which is an important subject of research. This exploration is relevant in paddy production, especially in the context of climate change where rice production needs to be intensified with reduced water application and with reduced methane emission. This chapter reviews the plastic response of roots and illustrates some preliminary findings on the effects of biotic (soil microbes) and abiotic (water regimes) stimuli on root growth and activity and their relationships with shoot growth and its implications for mitigation of methane production without compromising grain yield.",book:{id:"8044",slug:"root-biology-growth-physiology-and-functions",title:"Root Biology",fullTitle:"Root Biology - Growth, Physiology, and Functions"},signatures:"Abha Mishra",authors:null},{id:"64055",doi:"10.5772/intechopen.81509",title:"Ensiling Alfalfa (Medicago sativa L.) and Orchard Grass (Dactylis glomerata L.) Forage Harvested at 08:00 or 14:00, without Wilting or 1 or 2 h Wilting and with or without Use of Bacterial Inoculant",slug:"ensiling-alfalfa-medicago-sativa-l-and-orchard-grass-dactylis-glomerata-l-forage-harvested-at-08-00-",totalDownloads:1084,totalCrossrefCites:2,totalDimensionsCites:2,abstract:"Alfalfa forage is difficult to ensile due to low water-soluble carbohydrate content and high buffering capacity. The objective was to assess at Chapingo, Mexico, during the rainy season effects of combinations of harvest hours (08:00, 14:00), wilting time (0, 1, 2 h) and bacterial inoculants on the quality of silage made of alfalfa and orchard grass forage, made in 200-L containers. The experiment was conducted in three phases with two replicates per phase. Variables measured in freshly cut forage and silages were dry matter content (DM), buffer capacity, pH, and alcohol soluble carbohydrates (ASC). Silos remained sealed during 60 d, and additional variables measured in silage were aerobic stability, NH3 -N and in vitro disappearance of DM. In forage harvested at 14:00 h, DM and ASC contents were higher; pH and buffering capacity were not affected by harvest hour; in silages made of that forage, NH3-N levels were lower, while ASC contents and in vitro disappearance of MS were unaffected by harvest hour. Treatments with inoculants were less aerobic stable for 5 days when made of forage harvested at 08:00 h but more stable when made of forage harvested at 14:00 h. Harvesting at 14:00 h was advantageous as silage presented higher DM and ASC contents.",book:{id:"7491",slug:"forage-groups",title:"Forage Groups",fullTitle:"Forage Groups"},signatures:"Ricardo D. Améndola-Massiotti, Renato González-Ortiz, Luis A.\nMiranda-Romero, Juan A. Burgueño-Ferreira and Pedro Topete-\nPelayo",authors:[{id:"253852",title:"Dr.",name:"Ricardo D.",middleName:null,surname:"Améndola-Massiotti",slug:"ricardo-d.-amendola-massiotti",fullName:"Ricardo D. Améndola-Massiotti"},{id:"264572",title:"MSc.",name:"Renato",middleName:null,surname:"González-Ortiz",slug:"renato-gonzalez-ortiz",fullName:"Renato González-Ortiz"},{id:"264573",title:"Dr.",name:"Luis Alberto",middleName:null,surname:"Miranda-Romero",slug:"luis-alberto-miranda-romero",fullName:"Luis Alberto Miranda-Romero"},{id:"265415",title:"Dr.",name:"Juan",middleName:null,surname:"A. Burgueño-Ferreira",slug:"juan-a.-burgueno-ferreira",fullName:"Juan A. Burgueño-Ferreira"},{id:"265416",title:"Dr.",name:"Pedro",middleName:null,surname:"Topete-Pelayo",slug:"pedro-topete-pelayo",fullName:"Pedro Topete-Pelayo"}]}],mostDownloadedChaptersLast30Days:[{id:"63148",title:"Domestic Livestock and Its Alleged Role in Climate Change",slug:"domestic-livestock-and-its-alleged-role-in-climate-change",totalDownloads:15897,totalCrossrefCites:0,totalDimensionsCites:0,abstract:"It is very old wisdom that climate dictates farm management strategies. In recent years, however, we are increasingly confronted with claims that agriculture, livestock husbandry, and even food consumption habits are forcing the climate to change. We subjected this worrisome concern expressed by public institutions, the media, policy makers, and even scientists to a rigorous review, cross-checking critical coherence and (in)compatibilities within and between published scientific papers. Our key conclusion is there is no need for anthropogenic emissions of greenhouse gases (GHGs), and even less so for livestock-born emissions, to explain climate change. Climate has always been changing, and even the present warming is most likely driven by natural factors. The warming potential of anthropogenic GHG emissions has been exaggerated, and the beneficial impacts of manmade CO2 emissions for nature, agriculture, and global food security have been systematically suppressed, ignored, or at least downplayed by the IPCC (Intergovernmental Panel on Climate Change) and other UN (United Nations) agencies. Furthermore, we expose important methodological deficiencies in IPCC and FAO (Food Agriculture Organization) instructions and applications for the quantification of the manmade part of non-CO2-GHG emissions from agro-ecosystems. However, so far, these fatal errors inexorably propagated through scientific literature. Finally, we could not find a clear domestic livestock fingerprint, neither in the geographical methane distribution nor in the historical evolution of mean atmospheric methane concentration. In conclusion, everybody is free to choose a vegetarian or vegan lifestyle, but there is no scientific basis, whatsoever, for claiming this decision could contribute to save the planet’s climate.",book:{id:"7491",slug:"forage-groups",title:"Forage Groups",fullTitle:"Forage Groups"},signatures:"Albrecht Glatzle",authors:[{id:"252990",title:"Dr.",name:"Albrecht",middleName:null,surname:"Glatzle",slug:"albrecht-glatzle",fullName:"Albrecht Glatzle"}]},{id:"32711",title:"Flooding Stress on Plants: Anatomical, Morphological and Physiological Responses",slug:"flooding-stress-on-plants-anatomical-morphological-and-physiological-responses",totalDownloads:7796,totalCrossrefCites:0,totalDimensionsCites:0,abstract:null,book:{id:"1814",slug:"botany",title:"Botany",fullTitle:"Botany"},signatures:"Gustavo Gabriel Striker",authors:[{id:"93232",title:"Prof.",name:"Gustavo",middleName:"Gabriel",surname:"Striker",slug:"gustavo-striker",fullName:"Gustavo Striker"}]},{id:"65604",title:"Evaluation and Prediction of the Nutritive Value of Underutilised Forages as Potential Feeds for Ruminants",slug:"evaluation-and-prediction-of-the-nutritive-value-of-underutilised-forages-as-potential-feeds-for-rum",totalDownloads:1570,totalCrossrefCites:0,totalDimensionsCites:2,abstract:"The aim of the chapter was to evaluate and predict the nutritive and feeding value of unknown and underutilised forages. Underutilised forages were collected from various regions. Chemical composition and degradability of forages in the rumen were determined. A dataset was created bearing degradability parameters of feeds from 40 studies. Using the dataset, a step-wise regression procedure was used to develop regression equations to predict rumen degradability. Of the underutilised forages, crude protein content tended to be double for Brassica oleracea var. acephala compared to Colophospermum mopane leaves and pods. Forage grasses tended to have very low crude protein contents compared to legumes and concentrates. Underutilised Brassica oleracea var. acephala tended to have higher crude protein levels compared to commonly used protein sources. The regression model for predicting the soluble fraction accounted for 59% (development) and 71% (validation) of the variation. The regression model for predicting the potential degradability accounted for 65% (development) and 24% (validation) of the variation. In conclusion, the nutritive value of underutilised forages was good, high in crude protein and high potential degradability. After correcting for factors that significantly affected degradability parameters, predicted solubility and effective degradability lay near the ideal prediction line, giving good predictions.",book:{id:"7491",slug:"forage-groups",title:"Forage Groups",fullTitle:"Forage Groups"},signatures:"Mehluli Moyo, Siyabonga T. Bhiya, Masande Katamzi and Ignatius\nV. Nsahlai",authors:[{id:"201527",title:"Prof.",name:"Ignatius V.",middleName:null,surname:"Nsahlai",slug:"ignatius-v.-nsahlai",fullName:"Ignatius V. Nsahlai"},{id:"203798",title:"Mr.",name:"Mehluli",middleName:null,surname:"Moyo",slug:"mehluli-moyo",fullName:"Mehluli Moyo"},{id:"260135",title:"Mr.",name:"Katamzi",middleName:null,surname:"Masande",slug:"katamzi-masande",fullName:"Katamzi Masande"},{id:"283732",title:"Mr.",name:"Siyabonga",middleName:null,surname:"Bhiya",slug:"siyabonga-bhiya",fullName:"Siyabonga Bhiya"}]},{id:"76675",title:"Introductory Chapter: Studies on Cucumber",slug:"introductory-chapter-studies-on-cucumber",totalDownloads:447,totalCrossrefCites:0,totalDimensionsCites:1,abstract:null,book:{id:"9704",slug:"cucumber-economic-values-and-its-cultivation-and-breeding",title:"Cucumber Economic Values and Its Cultivation and Breeding",fullTitle:"Cucumber Economic Values and Its Cultivation and Breeding"},signatures:"Huixia Jia and Haiping Wang",authors:[{id:"280406",title:"Dr.",name:"Haiping",middleName:null,surname:"Wang",slug:"haiping-wang",fullName:"Haiping Wang"},{id:"417904",title:"Dr.",name:"Huixia",middleName:null,surname:"Jia",slug:"huixia-jia",fullName:"Huixia Jia"}]},{id:"64176",title:"Tropical Forage Legumes in India: Status and Scope for Sustaining Livestock Production",slug:"tropical-forage-legumes-in-india-status-and-scope-for-sustaining-livestock-production",totalDownloads:2010,totalCrossrefCites:3,totalDimensionsCites:6,abstract:"Livestock contributes enormously in food and nutritional security apart from livelihood security to rural population all over the world. India has the largest number of livestock, representing over 17% of world population. Availability of forage legumes is essential for better animal health, production and increasing the nutritive value of forage-based rations, besides providing a source of biological nitrogen fixation for enriching soil, reducing land degradation and mitigating climate change. However, supply of quality green fodder in India is extremely precarious, and the gap is huge against demand. The major fodder legume crops cultivated in India are Medicago sativa, Trifolium alexandrinum, Vigna unguiculata, Vigna umbellate and range legumes are Stylosanthes spp., Desmanthus virgatus, and Clitoria ternatea. 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He is an evaluator of project proposals for the European Union (H2020), Medical Research Council (MRC, UK), Spanish Government (ANECA, Spain), Research National Agency (ANR, France), DAAD (Germany), Argentinian Government, and the Colombian Institutions. He has been a reviewer in different indexed international journals (<70) and conferences (<250) since 2001. He has been a member of the IASTED Technical Committee on Image Processing from 2007 and a member of the IASTED Technical Committee on Artificial Intelligence and Expert Systems from 2011. \n\nHe has held the general chair position for the following: ACM-APPIS (2020, 2021), IEEE-IWOBI (2019, 2020 and 2020), A PPIS (2018, 2019), IEEE-IWOBI (2014, 2015, 2017, 2018), InnoEducaTIC (2014, 2017), IEEE-INES (2013), NoLISP (2011), JRBP (2012), and IEEE-ICCST (2005)\n\nHe is an associate editor of the Computational Intelligence and Neuroscience Journal (Hindawi – Q2 JCR-ISI). 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He won the “Catedra Telefonica” Awards in Modality of Knowledge Transfer, 2017, 2018, and 2019 editions, and awards in Modality of COVID Research in 2020.\n\nPublic References:\nResearcher ID http://www.researcherid.com/rid/N-5967-2014\nORCID https://orcid.org/0000-0002-4621-2768 \nScopus Author ID https://www.scopus.com/authid/detail.uri?authorId=6602376272\nScholar Google https://scholar.google.es/citations?user=G1ks9nIAAAAJ&hl=en \nResearchGate https://www.researchgate.net/profile/Carlos_Travieso",institutionString:null,institution:{name:"University of Las Palmas de Gran Canaria",institutionURL:null,country:{name:"Spain"}}},editorTwo:null,editorThree:null,series:{id:"14",title:"Artificial Intelligence",doi:"10.5772/intechopen.79920",issn:"2633-1403"},editorialBoard:[{id:"13633",title:"Prof.",name:"Abdelhamid",middleName:null,surname:"Mellouk",slug:"abdelhamid-mellouk",fullName:"Abdelhamid Mellouk",profilePictureURL:"https://mts.intechopen.com/storage/users/13633/images/1567_n.jpg",institutionString:null,institution:{name:"Paris 12 Val de Marne University",institutionURL:null,country:{name:"France"}}},{id:"109268",title:"Dr.",name:"Ali",middleName:null,surname:"Al-Ataby",slug:"ali-al-ataby",fullName:"Ali Al-Ataby",profilePictureURL:"https://mts.intechopen.com/storage/users/109268/images/7410_n.jpg",institutionString:null,institution:{name:"University of Liverpool",institutionURL:null,country:{name:"United Kingdom"}}},{id:"3807",title:"Dr.",name:"Carmelo",middleName:"Jose Albanez",surname:"Bastos-Filho",slug:"carmelo-bastos-filho",fullName:"Carmelo Bastos-Filho",profilePictureURL:"https://mts.intechopen.com/storage/users/3807/images/624_n.jpg",institutionString:null,institution:{name:"Universidade de Pernambuco",institutionURL:null,country:{name:"Brazil"}}},{id:"38850",title:"Dr.",name:"Efren",middleName:null,surname:"Gorrostieta Hurtado",slug:"efren-gorrostieta-hurtado",fullName:"Efren Gorrostieta Hurtado",profilePictureURL:"https://mts.intechopen.com/storage/users/38850/images/system/38850.jpg",institutionString:null,institution:{name:"Autonomous University of Queretaro",institutionURL:null,country:{name:"Mexico"}}},{id:"239041",title:"Prof.",name:"Yang",middleName:null,surname:"Yi",slug:"yang-yi",fullName:"Yang Yi",profilePictureURL:"https://mts.intechopen.com/storage/users/239041/images/system/239041.jpeg",institutionString:"Virginia Tech",institution:{name:"Virginia Tech",institutionURL:null,country:{name:"United States of America"}}}]},onlineFirstChapters:{paginationCount:34,paginationItems:[{id:"81595",title:"Prosthetic Concepts in Dental Implantology",doi:"10.5772/intechopen.104725",signatures:"Ivica Pelivan",slug:"prosthetic-concepts-in-dental-implantology",totalDownloads:22,totalCrossrefCites:0,totalDimensionsCites:0,authors:null,book:{title:"Current Concepts in Dental Implantology - 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\r\n\tIn general, the harsher the environmental conditions in an ecosystem, the lower the biodiversity. Changes in the environment caused by human activity accelerate the impoverishment of biodiversity.
\r\n
\r\n\tBiodiversity refers to “the variability of living organisms from any source, including terrestrial, marine and other aquatic ecosystems and the ecological complexes of which they are part; it includes diversity within each species, between species, and that of ecosystems”.
\r\n
\r\n\tBiodiversity provides food security and constitutes a gene pool for biotechnology, especially in the field of agriculture and medicine, and promotes the development of ecotourism.
\r\n
\r\n\tCurrently, biologists admit that we are witnessing the first phases of the seventh mass extinction caused by human intervention. It is estimated that the current rate of extinction is between a hundred and a thousand times faster than it was when man first appeared. The disappearance of species is caused not only by an accelerated rate of extinction, but also by a decrease in the rate of emergence of new species as human activities degrade the natural environment. The conservation of biological diversity is "a common concern of humanity" and an integral part of the development process. Its objectives are “the conservation of biological diversity, the sustainable use of its components, and the fair and equitable sharing of the benefits resulting from the use of genetic resources”.
\r\n
\r\n\tThe following are the main causes of biodiversity loss:
\r\n
\r\n\t• The destruction of natural habitats to expand urban and agricultural areas and to obtain timber, minerals and other natural resources.
\r\n
\r\n\t• The introduction of alien species into a habitat, whether intentionally or unintentionally which has an impact on the fauna and flora of the area, and as a result, they are reduced or become extinct.
\r\n
\r\n\t• Pollution from industrial and agricultural products, which devastate the fauna and flora, especially those in fresh water.
\r\n
\r\n\t• Global warming, which is seen as a threat to biological diversity, and will become increasingly important in the future.
",coverUrl:"https://cdn.intechopen.com/series_topics/covers/40.jpg",keywords:"Ecosystems, Biodiversity, Fauna, Taxonomy, Invasive species, Destruction of habitats, Overexploitation of natural resources, Pollution, Global warming, Conservation of natural spaces, Bioremediation"},{id:"39",title:"Environmental Resilience and Management",scope:"
\r\n\tThe environment is subject to severe anthropic effects. Among them are those associated with pollution, resource extraction and overexploitation, loss of biodiversity, soil degradation, disorderly land occupation and planning, and many others. These anthropic effects could potentially be caused by any inadequate management of the environment. However, ecosystems have a resilience that makes them react to disturbances which mitigate the negative effects. It is critical to understand how ecosystems, natural and anthropized, including urban environments, respond to actions that have a negative influence and how they are managed. It is also important to establish when the limits marked by the resilience and the breaking point are achieved and when no return is possible. The main focus for the chapters is to cover the subjects such as understanding how the environment resilience works, the mechanisms involved, and how to manage them in order to improve our interactions with the environment and promote the use of adequate management practices such as those outlined in the United Nations’ Sustainable Development Goals.
\r\n\tPollution is caused by a wide variety of human activities and occurs in diverse forms, for example biological, chemical, et cetera. In recent years, significant efforts have been made to ensure that the environment is clean, that rigorous rules are implemented, and old laws are updated to reduce the risks towards humans and ecosystems. However, rapid industrialization and the need for more cultivable sources or habitable lands, for an increasing population, as well as fewer alternatives for waste disposal, make the pollution control tasks more challenging. Therefore, this topic will focus on assessing and managing environmental pollution. It will cover various subjects, including risk assessment due to the pollution of ecosystems, transport and fate of pollutants, restoration or remediation of polluted matrices, and efforts towards sustainable solutions to minimize environmental pollution.
\r\n\tWater is not only a crucial substance needed for biological life on Earth, but it is also a basic requirement for the existence and development of the human society. Owing to the importance of water to life on Earth, early researchers conducted numerous studies and analyses on the liquid form of water from the perspectives of chemistry, physics, earth science, and biology, and concluded that Earth is a "water polo". Water covers approximately 71% of Earth's surface. However, 97.2% of this water is seawater, 21.5% is icebergs and glaciers, and only 0.65% is freshwater that can be used directly by humans. As a result, the amount of water reserves available for human consumption is limited. The development, utilization, and protection of freshwater resources has become the focus of water science research for the continued improvement of human livelihoods and society.
\r\n
\r\n\tWater exists as solid, liquid, and gas within Earth’s atmosphere, lithosphere, and biosphere. Liquid water is used for a variety of purposes besides drinking, including power generation, ecology, landscaping, and shipping. Because water is involved in various environmental hydrological processes as well as numerous aspects of the economy and human society, the study of various phenomena in the hydrosphere, the laws governing their occurrence and development, the relationship between the hydrosphere and other spheres of Earth, and the relationship between water and social development, are all part of water science. Knowledge systems for water science are improving continuously. Water science has become a specialized field concerned with the identification of its physical, chemical, and biological properties. In addition, it reveals the laws of water distribution, movement, and circulation, and proposes methods and tools for water development, utilization, planning, management, and protection. Currently, the field of water science covers research related to topics such as hydrology, water resources and water environment. It also includes research on water related issues such as safety, engineering, economy, law, culture, information, and education.
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Biochemistry also studies small signaling molecules, coenzymes, inhibitors, vitamins, and hormones, which play roles in life processes. Biochemical experimentation, besides coopting classical chemistry methods, e.g., chromatography, adopted new techniques, e.g., X-ray diffraction, electron microscopy, NMR, radioisotopes, and developed sophisticated microbial genetic tools, e.g., auxotroph mutants and their revertants, fermentation, etc. More recently, biochemistry embraced the ‘big data’ omics systems. Initial biochemical studies have been exclusively analytic: dissecting, purifying, and examining individual components of a biological system; in the apt words of Efraim Racker (1913 –1991), “Don’t waste clean thinking on dirty enzymes.” Today, however, biochemistry is becoming more agglomerative and comprehensive, setting out to integrate and describe entirely particular biological systems. 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Thus proteomics, an area of research that detects all protein forms expressed in an organism, including splice isoforms and post-translational modifications, is more suitable than genomics for a comprehensive understanding of the biochemical processes that govern life. The most common proteomics applications are currently in the clinical field for the identification, in a variety of biological matrices, of biomarkers for diagnosis and therapeutic intervention of disorders. From the comparison of proteomic profiles of control and disease or different physiological states, which may emerge, changes in protein expression can provide new insights into the roles played by some proteins in human pathologies. Understanding how proteins function and interact with each other is another goal of proteomics that makes this approach even more intriguing. Specialized technology and expertise are required to assess the proteome of any biological sample. 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