一类基于有界算子合成的模糊关系方程  

A Kind of Fuzzy Relational Based on Bounded Operators Composition

作　　者：陈伟[1] 吴望名[2] 

机构地区：[1]上海大学理学院,上海200436 [2]上海师范大学数学科学学院,上海200234

出　　处：《模糊系统与数学》2001年第2期13-20,共8页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目 (6 98730 34 )

摘　　要：讨论模糊关系的有界和 -有界积合成的基本性质。对于论域 U上的一个自反和有界传递的模糊关系 R,证明它是一个预序关系。得到关于有界算子的模糊线性方程有解的充要条件及解的递归结构。在此基础上给出有限论域上的模糊关系方程In this paper,we discuss the basic properties of bounded sum bounded product composition of fuzzy relations. For a reflexive and bounded transitive fuzzy relation R , we prove that R must be a preorder relation. Moreover, a sufficient and necessary condition to a fuzzy linear equation based on bounded operators has a solution and a recurrent structure of the solution set are proposed.Finally,we provide a procedure to find the solution sets of fuzzy relational equations based on bounded operators composition on finite universes.

关 键 词：模糊关系 有界合成 模糊关系方程 有界算子 有界和 有界积 模糊集理论 

分 类 号：B815.6[哲学宗教—逻辑学] O159[理学—数学]