The optimal approximation of fuzzy tolerance relation

Authors:
Ling Zhang;Yan-Ping Zhang;Shu Zhao
Affiliations:
School of Computer Science and Technology, Anhui University, Hefei, Anhui, P.R. China;School of Computer Science and Technology, Anhui University, Hefei, Anhui, P.R. China;School of Computer Science and Technology, Anhui University, Hefei, Anhui, P.R. China
Venue:
RSKT'11 Proceedings of the 6th international conference on Rough sets and knowledge technology
Year:
2011

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Abstract

A problem of the optimal approximation to a fuzzy tolerance relation is discussed in this paper. Specifically, our aim is to get the optimal fuzzy equivalence relation from a given fuzzy tolerance relation. Firstly, we discuss the relationship between the covering and the partition of a set. Then, we give the concept of distance between coverings (or partitions) and put forward the algorithms to get the optimal partition from a given covering. Main results include: 1) give the sufficient and necessary conditions for the optimal approximation of coverings in union sets; 2) give the necessary condition for absolutely optimal approximation of coverings; 3) based on the optimal approximation of each covering in the covering chain, the optimal fuzzy equivalence relation is obtained from the given fuzzy tolerance relation.