模糊等价关系下的模糊粗糙群

【作者】 高井贵；

【导师】 张振良； 陈世联；

【作者基本信息】 昆明理工大学 ， 系统理论， 2003， 硕士

【摘要】 将粗糙结构与经典代数结构，拓扑结构，序结构不断整合必将涌现出新的富有生机的数学分支，目前粗糙结构与经典代数结构结合起来的研究已有文章出现。Kuroki N研究了半群中的粗理想。首次提出了粗子半群和粗理想的概念，证明了同余关系下，半群的粗糙集是半群，左(右，双)理想的粗糙集是左(右，双)理想，并首次提出了粗子群和正规粗子群的概念，证明了在经典群中一固定的经典的正规子群所决定的同余关系下，子群的粗糙集是子群，正规子群的粗糙集是正规子群。粗糙结构与模糊代数结构结合起来的研究也已有文章出现，如张京玲研究了，在一经典群中一固定的经典正规子群所决定的同余关系下，模糊子群的粗糙集是模糊子群，模糊正规子群的粗糙集是模糊正规子群。 本文在以上的研究的基础之上，首次研究了在模糊等价关系下，粗糙集理论与模糊代数结构的关系，得出了在一经典群中一固定的模糊正规子群决定一个模糊等价关系，两个模糊正规子群决定的两个模糊等价关系的合成等于这两个模糊正规子群的积所决定的模糊等价关系，在一经典群中一固定的模糊正规子群所决定的模糊等价关系下，模糊子群的粗糙集是模糊子群，模糊正规子群的粗糙集是模糊正规子群，和模糊粗糙集的一些有意义的结论。 在此基础之上本文又首次提出了T模糊粗子群的概念。T模糊正规子群决定一个T模糊等价关系，两个T模糊正规子群决定的两个T模糊等价关系的合成等于这两个T模糊正规子群的积所决定的T模糊等价关系，并证明了在经典群中一固定的T模糊正规子群所决定的T模糊等价关系下，与模糊粗糙集相似的结论。更多还原

【Abstract】 Connected Rough structure with Algebra structure, Topology structure and order structure, many new prosperous mathematics branches will appear currently, there have been some articles on connecting Rough structure with Algebra structure. Rough ideals in a semigroups, Rough ideals been first introduced by KuroKi N. Under the condition of the congruence relation, Rough sets of a subsemigroup was proved to be its subsemigroup , while that of a left (right, besides ) ideals was also proved to be its a left (right, besides ) ideals, next, Rough sets in a group first introduced. Under the condition of the congruence relation determined by a given normal subgroup in a group, Rough sets of a subgroup was proved to be its subgroup, while that of a normal one was also proved to be its normal subgroup. Connected Rough structure with Fuzzy Algebra structure, there also have been some articles on connecting Rough structure with Fuzzy Algebra structure by zhang Jinglin. Under the condition of the congruence relation determined by a given Fuzzy normal group in a group, Rough sets of a Fuzzy subgroup was proved to be its Fuzzy subgroup, while that of a Fuzzy normal group was also proved to be its a Fuzzy normal group.In this paper, under the condition of the Fuzzy congruence relation determined by a given Fuzzy normal subgroup in a group, Connecting Rough structure with Algebra structure was discussed. It is proved that Under the condition of the fuzzy congruence relation determined by a given Fuzzy normal subgroup in a group, Rough sets of a Fuzzy subgroup was a Fuzzy subgroup, while that of a Fuzzy normal group was also proved to be its a Fuzzy normal group. Next T fuzzy congruence relation, T fuzzy Rough sets properties been first introduced in this paper and get some similar results.更多还原