软集与模糊集的格  

On lattices of soft sets and fuzzy sets

作　　者：柳晓燕[1] 

机构地区：[1]西安邮电大学理学院,陕西西安710121

出　　处：《西安邮电大学学报》2015年第4期74-79,共6页Journal of Xi’an University of Posts and Telecommunications

基　　金：国家自然科学基金资助项目(11301415);陕西省青年科技新星计划资助项目(2014KJXX-73)

摘　　要：从格论角度研究软集的一些代数性质,证明了给定论域上的全体软集可构成正交模格及布尔代数等格结构。依此指出给定论域上全体模糊集的格可嵌入全体软集的格,基于格论刻画了软集与模糊集之间的内在联系。Some algebraic properties of soft sets are investigated in this paper from a lattice-theoretical point of view. It is shown that the class of all soft sets over a given universe can form lattice structures including orthomodular lattices and Boolean algebras. In addition, it is pointed out that the lattice of fuzzy sets can be embedded into the lattice of soft sets, which characterizes some inner connections between soft sets and fuzzy sets based on lattice theory.

关 键 词：软集 模糊集 格 布尔代数 正交模格 

分 类 号：TP18[自动化与计算机技术—控制理论与控制工程]