A new kind of fuzzy relation equations based on inner transformation

✍ Scribed by Hong-Xing Li; Zhi-Hong Miao; Song-Chol Han; Jia-Yin Wang

• Publisher: Elsevier Science
• Year: 2005
• Tongue: English
• Weight: 719 KB
• Volume: 50
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/j.camwa.2004.10.049

✦ Synopsis

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 tuner transformation by a fuzzy relation are introduced, and also what is a fuzzy relation equation based on inner transformation ~s described Second, the discriminative matrix and the discriminative vector are defined. On the basis of them, an approach of discriminating whether such a fuzzy relatlon equation has nonzero solution is obtained. At last, a procedure of solving such fuzzy relation equations is presented. The solution set of a fuzzy relatmn equation based on tuner transformation is not closed with respect to join and meet operations, in general This shows that the tradltmnal methods being used for solving V-A composite fuzzy relatmn equations cannot be apphed into the study of this kind of fuzzy relation equatmns based on tuner transformatlon @