论文信息 - A Novel Representation of Fuzzy Equivalence Relation

A Novel Representation of Fuzzy Equivalence Relation

In order to construct fuzzy equivalence relation conveniently,in this paper, we study on the representation of fuzzy equivalent relation. On the basis of resolution structure theory (H. X. Li, Fuzzy clustering method based on perturbation, Fuzzy Sets and Systems vol. 33, pp. 291-302, 1989.),we construct two diagrams named parameter system and resolution system. And we propose and prove that the parameter system and its corresponding resolution can be used to represent a fuzzy equivalence relation. In addition,we also give two construction algorithms,and study the properties of them.

Guannan Deng | Yanli Jiang

[1] M. Dasgupta,et al. Factoring fuzzy transitivity , 2001, Fuzzy Sets Syst..

[2] Sergei Ovchinnikov,et al. Numerical representation of transitive fuzzy relations , 2002, Fuzzy Sets Syst..

[3] L. Hongxing. Fuzzy clustering methods based on perturbation , 1989 .

[4] Jordi Recasens,et al. Transitive closure and betweenness relations , 2001, Fuzzy Sets Syst..

[5] Marc Roubens,et al. Structure of transitive valued binary relations , 1995 .

[6] Zhongzhi Shi,et al. Fuzzy clustering method based on perturbation , 2003 .

[7] Sukhamay Kundu. A representation theorem for min-transitive fuzzy relations , 2000, Fuzzy Sets Syst..