基于下重截集的粗糙模糊集的构造性质  

Constructive Properties of Rough Fuzzy Sets Based on Lower Weight Level Sets

作　　者：何天荣 缪彩花 吴湘云 He Tianrong;Miao Caihua;Wu Xiangyun(Lijiang Teachers College,Lijiang 674199,Yunnan)

机构地区：[1]丽江师范高等专科学校,云南丽江674199

出　　处：《丽江师范高等专科学校学报》2020年第4期85-91,共7页Journal of Lijiang Teachers College

基　　金：云南省教育厅科学研究基金教师类项目《粗糙模糊集构造性质的推广研究》(2019J0384)。

摘　　要：文献[3]从"邻域"和"重域"的观点引入了三种新的截集:下截集,下重截集和上重截集,并把经典模糊集的截集称为上截集,给出了模糊集基于这些截集的分解定理,表现定理和扩展定理。文献[6]引入了粗糙模糊集的-上截集,-下截集,-下重截集和-上重截集;定义了粗糙模糊集的交与并的表示,并给出了交与并的表示下基于四种截集形式的粗糙模糊集的分解定理。笔者曾在[5]系统研究了基于并的粗糙模糊集四种截集形式的表现定理及扩张定理并给出理论证明。本文引入了粗糙模糊集交的表示形式下基于下重截集的分解定理,并系统研究了基于交的粗糙模糊集下重截集形式的构造性质,即研究了交的定义下粗糙模糊集的表现定理和扩展原理,并给出详细的理论证明。它是粗糙模糊集的表现定理的另一种表现形式,是粗糙模糊集构造性质的推广研究。reference[3],three new level sets are introduced from the viewpoint of"neighborhood"and"multiple domain":lower level set,lower weight level set and upper weight level set.The level set of classical fuzzy set is called upper level set,giving the decomposition theorem,representation theorem and extended theorem of fuzzy set based on these level sets.In reference[6],λ-upper level set,λ-lower level set,λ-lower weight level set,λ-upper weight level set are introduced;the representation of intersection and union of rough fuzzy sets is defined,and the decomposition theorem of rough fuzzy sets based on four kinds of level sets is given.In[5],the author has systematically studied the representation theorem and extended theorem of four level sets of rough fuzzy sets based on union,and has given theoretical proofs.In this paper,we introduce the decomposition theorem based on the lower weight level set under the representation of intersection of rough fuzzy sets,and systematically study the constructive properties of the lower weight level set of rough fuzzy sets based on intersection,that is,we study the representation theorem and extended principle of rough fuzzy sets under the definition of intersection,and give detailed theoretical proofs.It is another representation of the representation theorem of rough fuzzy sets and a generalization of the constructive properties of rough fuzzy sets.

关 键 词：粗糙模糊集 下重截集 交的表示 表现定理 扩展原理 

分 类 号：O15[理学—数学]