【作者】 张琳；

【导师】 王学平；

【作者基本信息】 四川师范大学 ， 基础数学， 2007， 硕士

【摘要】 本文讨论了[0,1]格上@-Fuzzy双线性方程的解集及模糊关系R的σ分解问题.首先对定义在[0,1]格上有限的@-Fuzzy双线性方程作了讨论,给出了@- Fuzzy双线性方程解的一些性质,并进一步刻画了方程的整个解集和结果集.接着,对定义在[0,1]格上无限的@-Fuzzy双线性方程的解集性质作了讨论,并进一步给出了当论域无限,X =且G(r) =时,@- Fuzzy双线性方程的部分解集.最后,对定义在[0,1]格上模糊关系R的σ分解问题作了讨论,给出了模糊关系R可σ分解的充要条件,然后在R = AσB时,给出了A与B的解集.更多还原

【Abstract】 In this paper, we deal with the solution sets of @-Fuzzy bilinearequations on [0,1] and theσ-decomposition of a fuzzy relation R. In par-ticular, we deal with the finite @-Fuzzy bilinear equations on [0,1]. Someproperties of @-fuzzy bilinear equations are given, then the solution sets andthe result associated with the solution sets of @-fuzzy bilinear equations areobtained. Further, we deal with the infinite @-Fuzzy bilinear equations on[0,1]. Some properties of @-fuzzy bilinear equations are given, then whenX = and G(r) = , the solution sets are obtained. In the end, we dealwith theσdecomposition problem of a fuzzy relation R on [0,1] . First,a necessary and sucient condition that a fuzzy relation R isσdecom-posable is given. Then the solution sets of A and B with AσB = R are obtained.更多还原