Theoretical and applicational aspects of fuzzy implication functions

Abstract

Fuzzy implication functions are one of the main mathematical operations in fuzzy logic. They generalize the classical two-valued implication, which takes values in {0, 1}, to fuzzy logic, where the truth values belong to the unit interval [0, 1]. This family of functions plays a significant role in the development of fuzzy systems. The study of this class of operations has been extensively developed in the last 40 years from both theoretical and applicational points of view. In our presentation we will concentrate on both streams. Firstly, we present the mathematical aspects of fuzzy implications, namely, analytical and algebraic.