模糊软矩阵及其格结构  

Fuzzy soft matrix and its lattice structure

作　　者：杨伟[1] 

机构地区：[1]临沂师范学院理学院,山东临沂276005

出　　处：《辽宁工程技术大学学报（自然科学版）》2010年第5期721-723,共3页Journal of Liaoning Technical University (Natural Science)

基　　金：山东省自然科学基金资助项目(Q2008A01)

摘　　要：将经典的软集推广到模糊软集,在此基础上引入模糊软矩阵的概念来给出模糊软集的简便的矩阵表示,并利用模糊软集的模糊软矩阵来定义模糊软集的软交、软并和软补运算,对模糊软集的上述代数运算进行理论研究,证明了它们满足幂等律、交换律、结合律、分配律、吸收律、复原律、0-1律和对偶律,并通过实例说明对模糊软集而言,互补律不成立.特别地,证明了所有的模糊软矩阵在定义的软交、软并运算下构成有界分配格.由此发现,模糊软矩阵概念的引入不仅有利于模糊软集的表示而且使得模糊软集的全体具有很好的格代数性质.In this study,a soft set is generalized from crisp to fuzzy set,and a simple fuzzy matrix representation of fuzzy soft set is given. Furthermore,the operations of fuzzy soft sets such as soft intersection,soft union and soft complement are defined using fuzzy matrix. Some algebraical properties of idempotent,commutative,associative,distributive,absorptive,involutive,0-1,and De Morgan laws are obtained. A case study which does not satisfy complement law is presented. In particular,the set of all fuzzy soft matrices forming a bounded distributive lattice under the new soft intersection and soft union operations is proved. Therefore,the introduction of fuzzy soft matrix is not only advantageous for representing the fuzzy soft set,but also induces admirable lattice algebraical properties.

关 键 词：模糊软集 模糊软矩阵 软集 模糊集 分配格 

分 类 号：O159[理学—数学]