Mathematical Modelling and Fuzzy Logic

Abstract

Mathematical knowledge beginning with, very simple mathematical definitions to very complex expressions is necessary for mathematical modelling. The same reality is true for Fuzzy Logic. Researchers all over the world have to understand to some degree the fundamental concepts of advanced mathematics. Infinity, continuity, limit, theory of functions, symbolic logic, number theory, linear algebra, probability theory, and topology are some of these fundamental concepts. If any researcher without a sound mathematical background, applies only the Fuzzy Logic formulas, it will be very superficial. We have to keep in mind that to understand the mathematical philosophy of Fuzzy Logic, we must learn and digest a whole different area in mathematics. Like in every field of science understanding the main idea and philosophy of Fuzzy Logic is much more important than technical and operational features. Day by day the concept of Fuzzy Sets influences many different fields, particularly engineering systems, sociology, economy, semantics, data analysis, medicine, decision making, etc.