L-可定义集与L-粗糙概念格  

L-definable Sets and L-rough Concept Lattices

作　　者：杨凌云[1,2] 徐罗山[1] 

机构地区：[1]扬州大学,数学科学学院,江苏扬州225002 [2]徐州师范大学,数学科学学院,江苏徐州221116

出　　处：《模糊系统与数学》2011年第2期131-137,共7页Fuzzy Systems and Mathematics

基　　金：国家自然科学基金资助项目(10371106;60774073)

摘　　要：对基于剩余格L的L-形式背景引入了L-可定义集概念,研究L-可定义集的性质及其与L-粗糙概念之间的关系。给出L-可定义集的刻画;得到常值L-集均为L-可定义集的若干等价条件;证明全体L-可定义集在L-集包含序下是相应L-幂集格及L-粗糙概念格的子完备格;给出全体L-可定义集恰为全体L-粗糙概念外延的一个充要条件。In this paper,the notion of L-definable sets of an L-formal context based on residuated lattices is introduced.Properties of L-definable sets are investigated.Relationships of L-definable sets and L-rough concepts are given.Characterizations of L-definable sets and some sufficient and necessary conditions for constant L-sets to be L-definable sets are obtained.It is proved that the set of L-definable sets of an L-formal context in the order of L-set inclusion is a complete sublattice of the related lattice of the L-sets and a complete sublattice of the related L-rough concept lattice.A sufficient and necessary condition for the set of L-definable sets to be exactly the extents of the related L-rough concept lattice is also given.

关 键 词：剩余格 L-形式背景 L-粗糙概念格 L-可定义集 

分 类 号：O141[理学—数学] O153[理学—基础数学]