Solving Interval-valued Fuzzy Relation Equations

Solving systems of fuzzy relation equations is an important topic in fuzzy set theory. This paper studies the composite interval-valued fuzzy relation equations. After analyzing the properties of its solution set, we convert the fuzzy relation equations into a fuzzy relation inequality system and propose an efficient computational procedure to generate the whole solution set. Examples are included to illustrate the idea and algorithm. Key words: Fuzzy relation equations, Max-min composition, Composite interval-valued fuzzy relation equations. This research work was supported, in part, by the North Carolina Supercomputing Center, Cray Research Grant, and the National Textile Center Research Grant S95-2. 0 1 Introduction Let A = [a ij ], 0 a ij 1, be an m \Theta n-dimensional fuzzy matrix and b = (b 1 ; b 2 ; :::; b n ) T , 0 b j 1, be an n-dimensional vector. Then A and b define a system of fuzzy relation equations: x ffi A = b; (1) where "ffi" denotes the commonly used max-m..