A new kind of fuzzy relation equations based on inner transformation

Authors:
Hong-Xing Li;Zhi-Hong Miao;Song-Chol Han;Jia-Yin Wang
Affiliations:
-;-;Department of Mathematics, Beijing Normal University Beijing 100875, P.R. China and Department of Mathematics and Mechanics, Kim Il Sung University Pyongyang, D.P.R. Korea;-
Venue:
Computers & Mathematics with Applications
Year:
2005

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Abstract

This paper mainly deals with a new kind of fuzzy relation equations based on inner transformation. First, the inner projection of a fuzzy relation and the inner transformation by a fuzzy relation are introduced, and also what is a fuzzy relation equation based on inner transformation is described. Second, the discriminative matrix and the discriminative vector are defined. On the basis of them, an approach of discriminating whether such a fuzzy relation equation has nonzero solution is obtained. At last, a procedure of solving such fuzzy relation equations is presented. The solution set of a fuzzy relation equation based on inner transformation is not closed with respect to join and meet operations, in general. This shows that the traditional methods being used for solving V-@L composite fuzzy relation equations cannot be applied into the study of this kind of fuzzy relation equations based on inner transformation.