Introductory Chapter: Basic Properties of Fuzzy Relations
Constantin Voloşencu · IntechOpen eBooks · 2020
General aspectsTreating information using fuzzy logic has developed over the past 50 years, this mathematical theory being an interesting tool for researchers to solve complex scientific and technical problems.In these years, research has always yielded new results in the field of advanced fuzzy logic applications.Fuzzy logic has found applications in various sectors of human activity, such as, industry, business, finance, medicine, and in many scientific fields such as, machine learning, big data technologies, fuzzy control, expert systems, dynamic fuzzy neural networks, and others.Fuzzy logic provides a different way of dealing with mathematical calculus problems.In the case of fuzzy logic, conventional algorithms are replaced by a series of linguistic rules of the If (then) condition (conclusion).Thus, a heuristic algorithm is obtained, and human experience can be taken into account in the subject matter of the calculation.This introductory chapter aims to recall some basic notions, main properties of fuzzy relations.Fuzzy rule bases and fuzzy blocks may be seen as relations between fuzzy sets and, respectively, between real sets, with algebraic properties as commutative property, inverse and identity.The fuzzy relations are developed with different rule bases, fuzzy values, membership functions, inference, and defuzzification methods, and they may be characterized with transfer characteristic graphs.The book [1] can be considered a reference in the field.Other references may be taken in consideration [2][3][4][5].The author published also in the field [6].As advantages of fuzzy logic are useful in the calculations, we can list the following:• Development of fuzzy controllers without a complex mathematical modeling of the problem addressed• The possibility of implementing "human linguistic knowledge" on the application solved.• The possibility of using fuzzy logic for complex, nonlinear, and variable relations• The possibility of performing exceptional treatments, that is, changing the calculation strategies as a result of a change in the course of application• Possibility of using it when making decisions specific to artificial intelligence• Interpolation among rules, usable in exceptional treatments to change the scope of application