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中文摘要：
从对称的角度考虑,人们自然而然的考虑到R所包含的最大模糊等价关系,这就是传递核.针对模糊相似关系的传递核问题提出并证明其一些基本性质,说明任意模糊相似关系其传递核的存在性及不唯一性.同时,还讨论了传递核与传递闭包的关系,指出利用传递核和传递闭包进行聚类时面临的局限性.
英文摘要：
The transitive closure of fuzzy similarity relation R is the smallest fuzzy equivalent relation that contains R.From a symmetrical point of view,it is natural to ask for the largest fuzzy equivalence relation being contained by R,that is transitive opening.Focus on transitive opening,some of its basic properties were proposed,existence and non-uniqueness of transitive opening were proved.In addition,relationship between transitive opening and transitive closure were compared,localizations of transitive opening and transitive closure in fuzzy clustering were indicated.
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