2011 | OriginalPaper | Buchkapitel
The Optimal Approximation of Fuzzy Tolerance Relation
verfasst von : Ling Zhang, Yan-ping Zhang, Shu Zhao
Erschienen in: Rough Sets and Knowledge Technology
Verlag: Springer Berlin Heidelberg
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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.