AN OVERVIEW OF FUZZY MATHEMATICS AND FUZZY LOGIC

Abstract

The term Fuzzy mathematics is related to research and treatment of phenomenon of ambiguity. Fuzziness can be found in almost all areas of daily life, for example in statements, engineering, controller designing for a plant or a process, manufacturing, optimization and economy etc. It is however, particularly faced in all the areas in which human evaluation, understanding, judgement and decisions are required. Fuzzy concepts are some form of generalizations of mathematical concepts. Probability and possibility are the two complementary theories. The fuzzy principle states that everything is a matter of degree of membership. In terms of mathematics, fuzzy sets are sets whose elements have degrees of membership. Many real-world problems cannot be described and handled by the use of classical set theory and it includes all those involving elements with only partial membership of a set. Fuzzy set theory, on the other side, accepts partial memberships, and, therefore, in some sense it generalizes the classical set theory to some extent. The fuzzy set theory is a very natural extension of the classical set theory, and also is a rigorous mathematical notion.