Improvement of Validated Manufacturing Processes with Fuzzy Logic

Abstract

SMEs are essential entities for the economy of countries, so they need to implement strategies to maintain and achieve economic stability. Technology is a great support tool to achieve this. Still, entrepreneurs, generally acting empirically, need to determine which technology to select, how to do it, and its scope of implementation. Fuzzy logic is a technology adapted to human linguistic thinking, which served as a methodology in this case study to measure the degree of behavior given by the implementation of software and hardware in a company. The result of the research validated the benefits that the gradual implementation of the technology presented to the company in terms of utility, time, and quantity of production, which were related in degrees of uncertainty with variables that were labeled as “high,” “medium,” and “low.” The established membership was validated through fuzzy graphs, showing the company’s status, and adjusted with the appropriateness of the technology until profits were placed within the “high” range. Thus, fuzzy logic is a tool that helps measure variables in degrees of belonging, with words used by business people to make it more understandable. Furthermore, the data coding in fuzzy terms showed the prediction of the behavior of the variables adjusted with technological processes.

1. Introduction

Manufacturing processes in the manufacturing industry differ from other sectors by their materials, their machinery, and how they carry out operations. In general, a process can be defined as the change of properties of an object, ranging from geometry, hardness, state, and content in the form of information data [1]. In the manufacturing industry, this definition applies perfectly.

The manufacturing industry is a vital sector for the countries’ economy and can be of different sizes: large, medium, and trim. In this context, small and medium-sized enterprises (SMEs) comprise a large percentage of all companies; Mexico has 4.9 million economic establishments, of which 98.8% are SMEs and generate 27 million jobs [2]. Other sources state that SMEs comprise 99.80% of the entire business fabric and generate 70% of employment. In addition, they contribute 50% of the Gross Domestic Product (GDP) [3], measure that expresses the monetary value of the production of goods and services demanded by a country or region during a given period.

In Latin America and the Caribbean, SMEs generate formal productive employment for 60% of workers, making up 99.5% of companies [4]. In the world, SMEs represent approximately 90% of companies, generating more than 50% of employment and 40% of GDP, according to the World Bank SME Finance [5]. In addition, the OECD determined that SMEs represent 60% of employment and between 50 and 60% of added value, which is why they are considered drivers of productivity in many regions [6].

In the background of the benefits of the companies, the PYMES are an essential part of a country’s economy. However, not all of them can survive the daily problems generated by the mismanagement of their processes, the inexperience of business people, and the nonexistence or poor adaptation of technology to support their businesses, is what can lead to the reduction of their profits, and to reaffirm this assertion [7], affirm that SMEs do not have practical management skills and have limited education and training of their workforce, so this type of problem often means that their life potential does not increase.

As a proposed solution to the above, innovation has created many types of technologies that would help increase their profits. Still, unfortunately, entrepreneurs do not know how to implement them since, by tradition, SMEs are made up of people who have acted empirically in the administration since their ancestors started them in a rustic or experimental way and without theoretical foundation and consequently, they are unaware of the benefits that it could give them and although the effects of technology on organizations and productivity in companies have not been analyzed for several years [8], it is time to return to them, mainly to explore the benefits of emerging technologies.

Manufacturing is one of our environment’s leading small and medium-sized companies. Only in Mexico in the fourth quarter of 2022, the population employed in these was 9.59 million, registering a gross domestic product of 5.51 billion pesos. If you look further back, in 2019, there were a total of 579,828 economic units in Manufacturing Industries, according to the website of the Government of Mexico [9]; this was the reason to focus this study on them and thus implement improvement strategies in their processes so that they continue to exist and progress.

For SMEs to achieve stability and growth, their problems are detected to generate new ideas to improve their manufacturing processes; this is taking into account that five-sixths of the world population, equivalent to 6 billion people, live in emerging countries and better products are required [10]; Therefore, it is necessary to improve the quality of processes and their products, to satisfy consumers and, consequently, improve the productive life of companies.

The productive processes have been studied for their improvement, implementing several techniques. Favela-Herrera et al. [11], created a lean manufacturing model as an alternative to increase productivity and develop manufacturing skills, where the results were observed mainly in the increase in operational performance that reduced production costs, but this was only in theory.

In other contexts, Chinese manufacturing companies have opted for technological innovation strategies in the manufacturing industry, strengthening official industry-university-research-customer cooperation and taking advantage of the Industry 4.0 era [12]. This idea should be used in other countries, starting with Universities, since they can be great allies of companies and become business advisors. Even so, while that happens, it is necessary to propose solutions to ensure that SMEs continue to generate economic benefits for countries.

Regarding the evolution of industries, in recent years, they have met various requirements that satisfy the market’s growing demands, so they must constantly evolve, trying to have innovation, greater productivity, and lower losses. For this, industrial researchers have been attempting to implement technology in manufacturing, where innovation requirements must cover logistics and administration aspects that encompass the production, supply, and distribution of materials used for manufacturing [13, 14]. However, it is essential to add methods to measure the results of this implementation and thus know if these changes are positive for companies and to what extent, as well as demonstrate to other companies that they can replicate the methodology with the confidence they already have.

The productive processes of a company were automated, attending to the strategies generated from an analysis based on fuzzy cognitive maps, from which the “consequents” generated from problems used as “background” were taken. A “case study” was carried out to analyze the benefits of innovation, review the results, and adjust the changes that technology made in the company, considering that everything can improve more and more, but being able to predict the best behavior from the study of the company in such a way that the change benefits the employer and its employees.

The study was achieved by analyzing the evolutionary process of the company, for which it was necessary to continuously adjust the changes, which make companies more mature and competitive; Socconini Luis [15] suggests that the adjustments made to companies should be corrective, prevention, improvement and innovation actions and, with this idea, an investigation proposing fuzzy models as a methodology, this to measure the results, in variables that can be adjusted as required by the innovation process.

A study was made of a family business with 20 workers, making it a small business. In this type of company, the leaders fulfill multiple complex functions that include the control of the company, although they still need a vision of the perspective of long-term growth. Instead, they see it as self-employment [16]. However, this idea is correct because this job earns money to live; it differs from what is required for its growth.

In the study company, the leaders need a comprehensive vision of growth and less of how to include technology since they need to see the antecedents and consequences to make decisions about its implementation. So, based on already established strategies, technology was implemented in the company to meet the most urgent needs and thus measure the benefit in terms of three selected study variables: production, time, and profits, which are essential for the company’s growth.

With these parameters, diffuse linguistic variables were established by low, medium, and high categories related to the study variables and modeled under the fuzzy logic scheme. Results were obtained that show the benefit that technology gave to the company, which at the end of the study was reflected in high terms in company profits, low in production and management time, and high in terms of quantities produced.

With this study, it was possible to appreciate that with the fuzzy methodology, the company’s behavior can be measured in terms of human language and adjust variables with the implementation of technology and forecast results.

2. Background

Fuzzy logic is a theory given by Lofti Zadeh in 1965, which is based on sets that have degrees of membership in them and are encoded in unitary intervals; that is, they have a membership function whose values are compatible with those sets in degrees of membership from 0 to 1. [17], mentions that this theory differs from classical logic, in that the data are complex, that is, a data has membership in a set, “all or nothing.”

Classical logic is based on sets where their inclusion is resolved in degrees of “true or false,” 0 or 1, all or nothing; unlike fuzzy logic, where a piece of data is part of a set to a certain extent, to a greater degree (0), sometimes to a medium degree (0.5) or can increase or decrease its vagueness, it can even be empty.

Classical logic has solved many problems, but it is necessary to solve those in which the membership of the data in a set is uncertain or, more specifically, in which they may belong to that set to a greater or lesser extent. To categorize elements into small or large with complex data, it would be said drastically and according to an established criterion, what is less or significant; However, how much do they cost? Who are they compared to? How small or big are they?; For example, if the number of employees of a company is measured and it is established that to be a “microenterprise” it must have 10 employees and to be “small” it must have more than 10, then a company with 13 employees, how small or what? Is it so big?

Most of the logic of human reasoning is not the classical logic of two values or even of several values rather, it is a logic of fuzzy truths, of fuzzy conjunctions, of fuzzy rules of deduction [18]. Fuzzy information locates its elements in degrees of belonging to one set or another, which means that in linguistic terms, not everything is genuine and not everything is false; that is, with this fuzzy logic, if a company has 13 employees, then it belongs to a certain degree to the small ones, although it is also part of the microenterprises to a greater degree, this example is shown analogically in Table 1.

Microenterprises
0.0	0.1	0.2	0.3	0.4	0.5	0.6	0.7	0.8	0.9	1.0
					Small companies

Table 1.

Example of the location of companies with fuzzy logic.

Source: prepared by the authors.

Fuzzy logic manages the vagueness of the sets according to their degree of membership; for example, people would be classified into wide and thin. The thin membership set is translated linguistically with If-Then-Else statements. This technique has also been applied in various contexts, both electronic and in other sectors belonging to the social or health sciences. There are three fuzzy inference classification systems (FIS), which are Mamdani FIS, TSK/Sugeno FIS, and Tsukamoto FIS, and they have variations.

Ebrahim Mamdani’s algorithm, proposed in 1974, maintains the “IF-THEN” rules given by linguistic expressions. Hence, its rule is “IF X is A THEN Y is B. Mamdani systems are made up of IF-THEN rules of the form “IF X is in A THEN Y is in B,“ such as “IF THE PRESSURE is HIGH THEN THE VOLUME is LOW.“ In these rules, the IF part “X is in A” is called the antecedent of the rule, and the THEN “Y are in B” part is called the consequent of the rule [19].

Rout et al. [20] describe the fuzzy inference model presented by Takagi, Sugeno, and Kang, called Sugeno and abbreviated TSK; it is based on three components: the rule base, the database, and the reasoning mechanism and its rules consist of antecedents and consequents that are stated “If A is antecedent then B is consequent, with a function that defines the degree of membership of an object and its rule is represented with a polynomial of the form: If there are two inputs “x” and “y,” the output polynomial will have the form z = px + qy + r and its rule is If x is A and B then z = f(x,y).

Suharjito and Yulyanto [21], describe the Tsukamoto FIS model presented in 1979; it is little known and therefore little used; it is a decision-making method with monotonic reasoning rules, that is, they are systems with a single rule of the form “Cause and Effect” or “Input-Output” implication in which the antecedent and consequence have to be correlated and uses the “centered average method.” An example of this model can be written as follows:

• If X is small then Y is C1

• If X is medium then Y is C2

• If X is big then Y is C3

As proposed, and based on the IF-Then denominator, fuzzy logic is a way of getting closer to human language since it handles vagueness in terms of words; the numbers are denoted in linguistic variables. Fuzzy data of some entities, for example, Table 2, shows the complex, imprecise data and their linguistic variables of the temperature of the day.

Hard value (classical logic)	Fuzzy value	Linguistic variable
1	1.0	Very hot
0	0.8	Hot
0	0.6	Warm
0	0.0	Very cold

Table 2.

Fuzzy values.

Source: prepared by the authors.

Another way of using fuzzy logic is through fuzzy cognitive maps (FCM), represented in a cognitive digraph that describes the behavior of a physical system in terms of nodes and edges that connect them and where each node of the graph is a fuzzy set described by variables, objects or entities of a system [22].

The FCM are oriented graphs, where a set of nodes represents notations in symbolic form and causal relationships in the form of weighted connections and, for the most part, the nodes are objects described by states or conditions, and the connections are actions or transfers functions, that transform a state in one node to another in another node; likewise, the FCM can be considered as a set of rules, where the input nodes are interconnected with the output ones and whose value corresponds to the consequent rule, and that data You can be represented in a knowledge matrix so that they are trained to obtain new values, all of this represented FCM as seen in Figure 1.

Figure 1.

Fuzzy cognitive map. Source [23].

Fuzzy logic has been used in multiple areas with multiple benefits for humanity. In the field of health, the help of this logic is shown by reducing the complexity of calculating the degree of similarity that may exist between diabetic patients who require different follow-up plans and proposing fuzzy decision trees that help the accuracy of this classification and thus improve the recovery step of case-based reasoning [24]. In addition, Fuzzy Logic has been used in contemporary designs by companies such as Eaton Industrial Controls, Motorola, NCR, Intel, Rockwell, Togai, and Nasa Gensym, among others, that use linear and nonlinear control, data analysis, pattern recognition, operations research, and financial systems [25].

The representation of the FCM has been done as shown in Figure 2, where a hybrid FCM is displayed to make time series forecasts, where it is observed that the input nodes are connected to a black box that improves the prediction rate and corrects the outputs and produces a better degree of confidence, based on metaheuristics.

Figure 2.

Hybrid classifier based on FCM type 1. Source [26].

In chemical processes, they have also been applied [27] to regulate the 3-valve liquid mixtures and thus obtain the best.

In other contexts, fuzzy logic has also been very beneficial for decision-making, applying it in social, governmental, or production fields through FCM. In social areas, FCMs have been used to analyze and solve problems related to the prediction of the socioeconomic consequences of privatization at the company level, where the opinions and expectations of the employees of the Nevşehir Alcoholic Beverage Factory of the General Directorate of Tekel, with the highest capacity in the Turkish distilled alcoholic beverages sector, in “If-Then” scenarios, to make predictions of variable interactions [28].

In this same vein, the FCM was also applied in case studies involving a complex phenomenon of poverty eradication and socioeconomic development strategies in rural areas under the DAY-NRLM (Deendayal Antyodaya Yojana-National Rural Livelihoods Mission) in India to be able to help policymakers to obtain precise results from proposed policies that address social resilience and sustainable socioeconomic development strategies [29].

3. Methodology

The project was implemented in a manufacturing company, and based on its problems analyzed through FCM, strategies were obtained that were implemented and adjusted to investigate their causes and effects. The description of the company and its issues are mentioned below to serve as a basis for the fuzzy analysis that was carried out.

3.1 Analysis

The Protexjd company is a company with 2 years of life, which belongs to the SMEs category, its business activity is the manufacture of uniforms for other companies, it currently has 20 workers, and its problems are basically with administration and production, the same which are mentioned subsequently:

1. There is no record of monitoring inputs, outputs, and processes of the manufactured materials and garments.

2. The staff makes manufacturing errors because they need to remember what is explained to them regarding product preparation.

3. The characteristics of the garments are not stored, so you have to start by explaining their manufacture each time a garment arrives, even if it has already been done.

4. They do not have production monitoring to know how the production processes are going.

5. Lack of uniformity in staff training.

6. Perceptions must be checked, so they must know the money flow.

An FCM was structured for the company to obtain possible implementation strategies, obtaining the one shown in Figure 3.

Figure 3.

FCM of a manufacturing company. Source: [30].

After establishing the FCM, the causes and effects were analyzed, determining the following strategies so that the company can give a better performance.

If the technology is increased, then:

• Perceptions increase.

• Production and management time is reduced.

• The time of the inventory management process is reduced.

• The repository of competencies and specifications is expanded.

• Reduction of losses.

• Production monitoring is increased.

• Profits are increased.

From the strategies, the items that would serve as solution factors were determined, establishing as solution variables: Production time, management time, production profits, and management profits, which gave rise to the other base variables, which are essential to be able to analyze and forecast established benefits, as described in Table 3, which makes a relationship between strategies and solution items with fuzzy variables:

	Fuzzy value	Production	Management time	Utilities
With technology	1.0	High	Low	High
	0.7	Half	Half	Half
	0.3	Low	High	Low

Table 3.

Relationship of fuzzy values with solution strategies in linguistic terms.

Source: prepared by the authors.

3.2 Design

Based on the data in Table 3 and by the FCM in Figure 3, the degree of belonging to each set was determined, as observed in Table 4, where values were assigned to the linguistic variables to have parameters of measurement in the evaluation and forecasts of the operation of the company.

Item	Amount	Linguistic variable
Products	0–150	Low
	100–220	Half
	180–400	High
Time	0–3	Low
	2–4	Half
	3–6	High
utilities	0–2000 (Mexican pesos)	Low
1800–8000 (Mexican pesos)	Half	High
	4500–14,500 (Mexican pesos)

Table 4.

Linguistic variables of the system.

Source: prepared by the authors.

To know if the above is being handled properly and to determine forecasts for the use of technology, an analysis was made applying the fuzzy theory, precisely the Mandamni technique, which consists of having an antecedent and a consequent that is specified in the function:

If a is A1 and b is B1 then c is C1.

If a is A2 and b is B2 then c is C2.

Subsequently, the data in Table 3 were coded in Python, where the low, medium, and high values were established in production, time, and profit, which can be seen in Figure 4a–c, respectively. All this is according to the data given by the employer.

Figure 4.

Fuzzy representation of the linguistic data of (a) production, (b) time, and (c) utilities. Source: Prepared by the authors.

Afterward, the fuzzy rules based on Mandamni, shown in Figure 5, were applied to determine the base behavior of the variables. In the figure, it can be seen that the antecedent in rule 1 is “low production,” “high time,” and they have a consequence of “low profits”; in rule 2, “high production” and “low time” are antecedents of “high profits” which is consequent; and finally, rule 3, “average production” and “average time,” produce “average profits.”

Figure 5.

Fuzzy system rules. Source: Prepared by the authors.

After applying the rules, the analysis reflected that with the technology in the company, the production levels are “low,” and consequently, its profits as well, and obviously, the production and management time was categorized as “high.” The chart in Figure 6 shows that the initial profit level was about 1500 in 6 days, which gives a membership of 1.0, which is low.

Figure 6.

Fuzzy graph generated at the beginning of the company analysis. Source: Prepared by the authors.

With this panorama of data and to verify the innovation forecasts in the company, technology based on embedded systems was added, which consisted of the insertion of two intelligent sewing machines to improve profits to 4900, see Figure 7.

Figure 7.

Fuzzy graph resulting from the implementation of computerized machines. Source: Prepared by the authors.

Finally, technology based on production management systems was added, which controls the flow of products, orders, and deliveries. The design shows the basic operations of insertion and consultation of the products, which are added to the products that enter the company (see Figure 8a). In addition, the system shows the production orders along with their control data, which allows the current number of garments to be reflected and displays the result of the arithmetic operation of the inputs and outputs of products (see Figure 8b); in addition, the numbers that are stored in the product deliveries section are those that are displayed as final products to update the number of garments that remain to be delivered (see Figure 8c). This information system is essential for monitoring production management.

Figure 8.

Management information system. (a) Insertion of products (b) inputs and outputs of products (c) processes. Source: Prepared by the authors.

With this latest technology, the profits increased to 10,550 pesos in 6 days, as shown in Figure 9, which is marked with the black line, where you can see that the membership was approximately 0.7.

Figure 9.

Fuzzy graph resulting from the implementation of computerized machines and production management system. Source: Prepared by the authors.

4. Results

The company’s technology benefits are summarized in Table 5, which shows the state of the profits.

Phase	Production quantity	Time	Utilities (Mexican pesos)	Membership	Linguistic Variable
Start	100 products	6 days	$1500	1.0	Low
With embedded technology	220 products	6 days	$4900	0.8	Half
With information systems	320 products	6 days	$10,550	0.7	High

Table 5.

Analysis of the production process with fuzzy logic.

Source: prepared by the authors.

Table 5 shows the fuzzy logic analysis forecast, which suggests that the more significant the technological increase in the company, the more production and profits increase. That seems logical, but it is necessary to show business people how much the benefit of the increase could be so that it serves as a reference.

Concerning time, it decreases the initial quantities produced; that is, if 100 pieces were made at the beginning in 6 days, with technology, the production of those same products over time was reduced by 30 percent.

With the implementation of the first technology, production increased considerably by 120, and it is logical because these machines generate fewer errors fewer excess threads, and each process is done automatically.

They increased those of the second phase by more than 50% and, although it seems that it does not coincide with the products generated, which were 100 more, it is understandable, since the management of the system monitors production, and thus prevents the loss of garments or that they are paid twice. In addition, it controls the entries and exits of the inventory, both products and materials, derived from calculating the material that must be used based on the number of garments in the process. It helps save and avoid waste or theft. In the end, profits increased with a high membership of 0.7.

5. Discussion

The fuzzy logic establishes threshold data; in this study, it can be observed that the low membership is 1.0 for 80 products, but if the company produces from 0 to 150, they are in a low range. As the products increase, the “low” membership decreases to become “medium.” Analogically, in all phases (low, medium, and high), the same happens with all items of products, time, and profits.

In this way, it is known that if the production was 220 products, its membership was 0.8, that is, to be closer to being within the “high” production set.

In the profits, and considering these data, if the profits were 10,550, he had a membership of 0.8, which is regarded as “high.” In a hypothetical case, if the profits had been 7000, the membership would be approximately 0.3, considered high, but less than 0.8.

It is necessary to clarify that there is still a lack of technology to be implemented, which could not only improve profits but could even decrease the human emotional problem generated by production errors, but this analysis, valued in fuzzy logic, provides the basis for it to be used as a methodology to evaluate a company and forecast benefits based on parameters of each company.

6. Conclusions

SMEs support the economy around the world; therefore, looking for strategies to obtain the best results in different aspects is essential. In this case, the innovation occurred in manufacturing and production management. Manufacturing is one of the activities where there are microenterprises that collaborate with a larger company, and it is here where emphasis should be placed on manufacturing processes since their limitations are more significant when it comes to small companies, considering that they are companies formed generally by people who do not know much about technology, nor its benefits and obviously, nor how it could help them have better profits and fewer problems.

Fuzzy logic is proposed in this research chapter as a method that evaluates and validates the manufacturing processes of a company presented as an object of study. The technology incorporated into the company evaluates and validates the results, foreseeing that it can be further improved with the integration of more technology, which makes the company increasingly mature.

The fuzzy methodology was established through rules that manage degrees of uncertainty called “high,” “medium,” and “low,” selected by ranges of data that relate them to the variables “products,” “time,” and “utilities” that generate their variations.

The use obtained in each implementation stage was reflected in the analysis of the manufacturing process, comparing its results without and with the implementation of technology. It may be logical to know that technology brings benefits, but measuring the certainty of the company’s growth is necessary.

Fuzzy technology provides vagueness in the data, which provides certainty that it is within established parameters and gives entrepreneurs an idea of what the technology is doing for their businesses.

With embedded systems technology, one could have the idea that it serves to generate greater production and consequently greater profits, but it is necessary to determine how much the benefit is, in this case, in terms of products, time, and profits. With the information management system, it is not so easy for people to see its benefits, which, in this case, is less time to review the monitoring of production and the input and output of products. It seems simple, but having this knowledge generates less anxiety for microbusiness leaders since they always have in view the number of garments that remain to be delivered, those that have entered the company, and those that are still in production.

Fuzzy analysis clarifies data in the manufacturing process, showing benchmarks in production, time, and profits through languages understood by workers and measured in a language that provides an objective perspective to workers. Saying that production is low, time is short, and profits are high gives leaders a better idea of what they need to adjust in their processes.

The first time the company analysis data was obtained, a company with “low” profits was observed. When the fuzzy analysis of the second stage was carried out, where embedded systems were implemented through automated machines, the results showed graphs with an increase in profits that classified them as “medium.” In the third stage, when the information system for production management was implemented, profits reached the “high.”

For all of the above, it is concluded that systems analysis using fuzzy logic can show forecasts of the quantities involved, and this can help in planning and, consequently, in decision-making.

Finally, with this method, entrepreneurs could plan and invest in their companies with the certainty that they will be able to obtain profits in a certain time, generating confidence in their investments.

It is important to mention that based on the strategies generated by the analysis with the fuzzy cognitive map, it is necessary to increase the implementation of technology, but this way of measuring progress in the company provides entrepreneurs with the best expectation of the development of their company.; This model may vary from one company to another, but it is a reference for other companies, which, although they will have different data and technology, the results could occur in a similar way.

As already mentioned, SMEs are very important financial entities for the economic development of countries, and this diffuse method could help them grow to have more and better companies and, what is better, help companies survive.

Acknowledgments

Marisol Hernández-Hernández would like to express his appreciation for the support provided by the Technological Institute of Higher Studies of Ixtapaluca through its program of national postdoctoral stays coordinated by CONAHCYT (National Council of Humanities, Sciences, and Technologies).