Abstract

Fuzzy tolerance quotient space has advantages in processing incomplete data. In this paper, model of fuzzy tolerance granularity is discussed, a hierarchical structure is given, and best approximation of incomplete data is researched. Firstly, the distance between set cover and set partition is defined. Secondly, the best approximation of given cover is researched, and then corresponding best algorithm is given. Finally, fuzzy tolerance relation is transformed into tolerance relation chain by using quotient space method, and then best approximation of fuzzy equivalence relation for fuzzy tolerance relation is given by using the algorithm of best approximation to tolerance relation.

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