新型软BE-代数的研究  

New Type of Soft BE-algebras

作　　者：张瑜[1] 廖祖华 ZHANG Yu;LIAO Zu-hua(Jiangsu Vocational College of Information Technology,Wuxi 214153,China;School of Science,Jiangnan University,Wuxi 214122,China)

机构地区：[1]江苏信息职业技术学院,江苏无锡214153 [2]江南大学理学院,江苏无锡214122

出　　处：《模糊系统与数学》2021年第5期5-14,共10页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(61170121);江苏省自然科学基金资助项目(BK20151117);江苏省高等学校自然科学研究项目(19KJD100006)

摘　　要：本文首先将软集的参数集赋予了BE-代数的代数结构,给出了新型软BE-代数的概念;然后利用软集的且、交等运算,研究了它的基本性质;接着提出了两个BE-代数的并代数、两个软集在并代数上的扩展交以及两个软集的合成运算等新概念;研究了新型软BE-代数的软平移及投影等相关性质。此外,利用两个软集的合成运算、软集的水平集以及广义特征函数分别给出了新型软BE-代数的等价刻画。最后给出新型软BE-代数的同态像与原像之间的性质。In this paper,by means of endowing a parameter set with an algebraic structure of BE-algebra,the notion of a new type of soft BE-algebra is proposed firstly.Then some fundamental properties are discussed through the intersection and AND operation of soft sets・In addition,the new concepts of union algebra,extended intersection of two soft sets based on union algebra and composite operation of two soft sets are introduced.Some properties related to the soft translation and projection of BE-algebra are also investigated.Besides,by utilizing compositional operation,the level set of soft set and generalized characteristic function,the equivalent characterizations of the novel type of soft BE-algebra are given・Furthermore,the properties of the homomorphism image and inverse image of the new type of soft BE-algebra are discussed.

关 键 词：软集 软BE-代数 软集运算 并代数 软平移 投影 

分 类 号：O159[理学—数学]