THE CONCEPT OF Z FUZZY RELATION

Abstract

Fuzzy sets were developed as a generalization of usual sets to take into account the vagueness and uncertainty in everyday life. In 2011 Zadeh further extended the idea and introduced the concept of z-numbers which model the ‘fuzziness’ of information and in addition include the reliability factor. Simply put an z-number is an ordered pair of fuzzy numbers where the first component gives the information and the second component deals with the reliability of information.
Fuzzy versions of various mathematical concepts have been developed over the last few decades. Fuzzy relations have been well studied and they play a vital role in fuzzy logic. In this paper we extend the concept of fuzzy relation and introduce the Z fuzzy relation. We show how z fuzzy if-then rules can be described by z fuzzy relation. The generalized compositional rule of inference is also developed.
Z fuzzy relations have the potential for applications in theory of approximate reasoning, medical diagnosis etc.