模糊相似关系的传递核  

TRANSITIVE OPENING OF FUZZY SIMILARITY RELATION

作　　者：邓冠男[1] 王志高[2] 

机构地区：[1]北京师范大学数学科学学院,北京100875 [2]中国劳动关系学院,北京100048

出　　处：《北京师范大学学报（自然科学版）》2010年第2期111-114,共4页Journal of Beijing Normal University(Natural Science)

基　　金：国家自然科学基金资助项目(60774049)

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.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.

关 键 词：传递核 传递闭包 模糊相似关系 模糊等价关系 

分 类 号：O159[理学—数学]