一般关系诱导的模糊拓扑和模糊拓扑约简  

The Relationships between Fuzzy Topologies and Fuzzy Rough Sets

作　　者：赵晓霞[1] 冯艳宾[1] ZHAO Xiao-xia;FENG Yan-bin(School of Information Science,Beijing Language and Culture University,Beijing 100083,China)

机构地区：[1]北京语言大学信息科学学院,北京100083

出　　处：《模糊系统与数学》2021年第3期8-17,共10页Fuzzy Systems and Mathematics

基　　金：国家基金委项目(61972052);北京语言大学高峰团队项目(GF201905);北京语言大学校级项目(中央高校基本科研业务费专项资金)(17PT01)。

摘　　要：本论文主要研究一般模糊关系诱导的模糊拓扑以及模糊拓扑的性质。首先,我们给出一般模糊关系诱导的模糊拓扑τR的定义,并讨论模糊拓扑的基本性质,然后证明τR和τt(R∪I)是两个相同的拓扑。第二,得到τR的内部算子和闭包算子的具体表达式。此外还知道,当τ是quasi-离散拓扑时,τ上的模糊关系Rτ诱导的拓扑和τ是相同的。第三,考查模糊拓扑τR的一些拓扑性质。最后,我们还定义τR上模糊拓扑约简,给出约简的算法,并给予算法的证明。This paper is devoted to the discussion of fuzzy topologies induced by fuzzy relations.Firstly,the fuzzy topologyτR is defined by a fuzzy relation and is considered some elementary properties.Furthermore,τR coincides withτt(R∪I)in this paper.Secondly,the interior and closure operations ofτR are obtained respectively.Moreover,fuzzy topology induced by fuzzy relation Rτfrom topologyτis exactlyτif and if onlyτis quasi-discrete.Thirdly,the separation axiom is discussed for fuzzy topologyτR.Finally,a fuzzy topological reduction is defined which is based onτR,and an algorithm is proposed to compute all the reduction sets.

关 键 词：模糊拓扑 分离性定理 传递关系 传递闭包 

分 类 号：O189[理学—数学]