The approach called as “graph theory and matrix approach” has been well employed in numerous research studies with a view to perform the decision-making while the situation is becoming perplexed type or where there is a very strong relative importance of one parameter over another. In such cases, the said graph theory and matrix method provides very suitable and fruitful solutions to make the decision to its final effective extent. The further improvements and the outcome enhancement can also be revealed through the use of combined practice of graph theory results along with some artificial intelligence-inspired logics and practices such as fuzzy logic, artificial neural network, etc. The significance and applicability of said method in vast fields of science, engineering, and research are also proved. Nowadays, our manufacturing sectors are getting up to date through the applications of artificial intelligence and several software-based directions. This is all to enhance the overall machine system performance with a view to improve desired performance characteristics of the process under the study. Few sections of this chapter has also elaborated the utility of the artificial intelligence-inspired fuzzy logic-based decision system which has already been a part of previous researches.