模糊正则子半群的度量  

The Measure of Fuzzy Regular Subsemigroups

作　　者：王先婷[1] 廖祖华 WANG Xian-ting;LIAO Zu-hua(Department of Basic,Wuxi Institute of Technology,Wuxi 214121,China;School of Science,JiangNan University,Wuxi 214122,China)

机构地区：[1]无锡职业技术学院基础部,江苏无锡214121 [2]江南大学理学院,江苏无锡214122

出　　处：《模糊系统与数学》2020年第4期35-43,共9页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(61170121,11401259,61673193);江苏省自然科学基金资助项目(BK2015117);江苏省高等学校自然科学基金资助项目(19KJD100006)。

摘　　要：本文主要研究模糊正则子半群的度量问题,利用模糊正则子半群度讨论了正则半群的模糊子集是模糊正则半群的程度。首先,文章通过[0,1]上的蕴含给出了模糊正则子半群度的定义。其次,利用正则半群模糊集的(强)水平集得到了模糊正则子半群度的等价刻画。最后,讨论了任意多个模糊子集的交、直积的模糊正则子半群度以及正则半群的模糊子集在同态映射下像与原像的模糊正则子半群度的性质。In this paper, we mainly introduce a fuzzy regular subsemigroup degree and we discuss the degree to which a fuzzy subset of a regular subsemigroup is a fuzzy regular subsemigroup. Firstly, we give the definition of a fuzzy regular subsemigroup degree by means of the implication operator of [0,1]. Secondly, we discuss the equivalent characterizations of a fuzzy regular subsemigroup degree by the(strong) level set of fuzzy sets. Finally, we research the fuzzy regular subsemigroups degrees of the intersection and the direct products of fuzzy subsets and the properties of a fuzzy regular subsemigroup degree about the homomorphic image and inverse image of the fuzzy subset.

关 键 词：半群 正则半群 同态 模糊正则子半群度 R-蕴涵 

分 类 号：O159[理学—数学]