模糊相容关系的最优逼近问题

Best Approximation for Fuzzy Tolerance Relation

文中讨论模糊相容关系的最优模糊等价关系的逼近问题,先讨论集合覆盖与划分之间的关系,给出覆盖(划分)之间距离的概念,在此基础上提出求已知覆盖的最优划分逼近的问题,并讨论在三种不同的划分集合簇中求最优逼近的准则,给出了相应的最优算法.然后利用商空间方法将模糊相容关系化成相容关系链,再利用求相容的最优逼近的算法,给出求模糊相容关系的最优逼近的模糊等价关系.

In this paper, we investigate the fuzzy equivalence relation based optimal approxima- tion of a fuzzy tolerance relation. Firstly, we discuss the relation between covers and partitions on a set. Secondly, based on the concept of the distance between two covers （or partitions） of a set, we present the optimal partition approximation problem of a given cover and further discuss the problem under three different families of sets of partitions and their corresponding optimal algorithms. Finally, we show that a fuzzy tolerance relation can be transformed into a chain of tolerance relations by using quotient space method. Then, the optimal approximation algorithms of tolerance relations are used to obtain an optimal approximation of fuzzy equivalence relation from a fuzzy tolerance relation.