(∈,∈∨q)-直觉模糊向量子空间  

(∈,∈∨q)-intuitionistic fuzzy vector subspace

作　　者：张成[1] 刘晓真[1] 赵植武[1] 

机构地区：[1]大连大学信息工程学院,辽宁大连116622

出　　处：《辽宁工程技术大学学报（自然科学版）》2010年第5期736-739,共4页Journal of Liaoning Technical University (Natural Science)

基　　金：辽宁省教育厅高等学校科学研究项目(20060073)

摘　　要：为了建立直觉模糊向量子空间的统一理论,采用直觉模糊集截集理论和模糊点xa与直觉模糊集A的邻属关系,并利用三值Lukasiewicz蕴涵,给出了(α,β)-直觉模糊向量子空间的定义,由此可以得到16种直觉模糊向量子空间。研究结果表明:(∈,∈)-直觉模糊向量子空间和(∈,∈∨q)-直觉模糊向量子空间是其中两种非常有意义的直觉模糊向量子空间,给出了(∈,∈)-直觉模糊向量子空间和(∈,∈∨q)-直觉模糊向量子空间之间的关系,并得出了(∈,∈∨q)-直觉模糊向量子空间的相关性质。该成果突破了对原有直觉模糊向量子空间的认识,从而为直觉模糊分析理论研究打下基础。In order to establish a uniform theory for the intuitionistic fuzzy vector subspaces,based on the concept of cut sets on intuitionistic fuzzy sets and the neighborhood relations between a fuzzy point xa and an intuitionistic fuzzy set A ,the definitions of （α ,β ）-intuitionistic fuzzy vector subspaces are given by applying the 3-valued Lukasiewicz implication. Therefore,16 kinds of （α ,β ）-intuitionistic fuzzy vector subspace are obtained. The study result demonstrates that the significant ones are the （∈ ,∈ ）-intuitionistic fuzzy vector subspace and（∈,∈ ∨ q）-intuitionistic fuzzy vector subspace. In this paper,the relationship between（∈,∈） -intuitionistic fuzzy vector subspace and （∈,∈ ∨ q）-intuitionistic fuzzy vector subspace is discussed,and the properties of （∈ ,∈ ∨ q）-intuitionistic fuzzy vector subspace are provided. The study is a breakthrough in the original comprehension on intuitionistic fuzzy vector subspace and establishes a foundation for the intuitionistic fuzzy analysis theory.

关 键 词：直觉模糊集 直觉模糊集截集 Lukasiewicz蕴涵 (∈ ∈∨q)-直觉模糊向量子空间 

分 类 号：O159[理学—数学]