由普通导算子诱导的F导算子及由F导算子诱导的F拓扑  

THE FUZZY DERIVED OPERATOR INDUCED BY THE DERIVED OPERATOR OF ORDINARY SET AND FUZZY TOPOLOGY INDUCED BY THE FUZZY DERIVED OPERATOR

作　　者：史福贵[1] 

机构地区：[1]牡丹江师范学院

出　　处：《模糊系统与数学》1991年第1期32-37,共6页Fuzzy Systems and Mathematics

摘　　要：本文扩展了普通集X的导算子d的定义,诱导出了X的fuzzy导算子d,进而由d诱导出X的一个fuzzy拓扑■,证明了fuzzy拓扑空间(X,■)怡是由d诱导的分明拓扑空间(X,τ)拓扑生成的,对X的每个fuzzy导算子d,存在X的唯一拓扑■,使得对X的每个fuzzy子集A,其在(X,■)中的导集A^d恰是它在fuzzy导算子d下的象d(A)。In this paper, we extend the derived operator d of ordinary set X and induce a fuzzy derived operator d of X, hence obtain a fuzzy topology by the fuzzy derived operator d and prove this fuzzy topological space (X) is exactly topologically generated by crisp topological space (X, τ), in which crisp topology τ is induced by the derived operator d of X. For any fuzzy derived operator d of X, there is only a topology such that for any A∈I^x, its derived set A^d in (X) is exactly d (A).

关 键 词：普通集 模糊导算子 模糊拓扑空间 导算子 聚点 导集 

分 类 号：O189.3[理学—数学] O159[理学—基础数学]