From the algorithm procedure presented in section 4 and the examples in this section, we can nd out it is easy to solve interval valued fuzzy relation equations by using fuzzy relation inequality system (8). The computation complexity of this algorithm is as same as that of the more commonly used algorithm 5] for fuzzy relation equations (1). So, the problem is more complicated than constant fu...

the pioneer work of image compression/reconstruction based onfuzzy relational equations (icf) and the related works are introduced. theicf regards an original image as a fuzzy relation by embedding the brightnesslevel into [0,1]. the compression/reconstruction of icf correspond to thecomposition/solving inverse problem formulated on fuzzy relational equations.optimizations of icf can be consequ...

In this article, we develop a new method and an algorithm to solve a system of fuzzy relation equations. We first introduce a solution-base-matrix and then give a tractable mathematical logic representation of all minimal solutions. Next, we design a new universal algorithm to get them. Two simplification rules are found to simplify the solution-base-matrix. We show that a polynomial time algor...

Systems which use a fuzzy rule base and an inference mechanisms are quite frequently used in many applications. Fuzzy rules and inference mechanisms can be described by a system of fuzzy relation equations. A solution to a given system of fuzzy relation equations can serve us a proper model of fuzzy rules (fuzzy model for short). But only two particular solutions, let us call them disjunctive a...

In this paper, we eneralize our previous results regarding approximate solutions of fuzzy relation e uations [lo] to systems offuzzy relation equations. By employing the e uality index proposed by Gottwald 731, we introduce a goodness measure of the performance of approximate sAutions and derive a lower bound and an upper bound of solvability of s stems of fuzzy relation equations. We also show...

In this paper we investigate the System of fuzzy relation equations with inf → composition. We base on the knowledge of he system of fuzzy relation equations with sup−∗-composition. First, the general notions are explained and then are shown the smallest and maximal solutions. Finally is investigated a simple criterion of solvability for a special case of fuzzy sets.

This paper aims to solve the problem of multiple-objective linear optimization model subject to a system of inf-! composition fuzzy relation equations, where ! is R-, Sor QL-implications generated by continuous Archimedean t-norm (s-norm). Since the feasible domain of inf-! relation equations constraint is nonconvex, these traditional mathematical programming techniques may have difficulty in c...