区间集上非交换剩余格的〈∈,∈∪〉-fuzzy滤子及其特征刻画  

〈∈,∈∪〉-fuzzy filter and its characterization of the non-commutative residual lattices on the interval sets

作　　者：乔希民[1] 吴洪博[2] 

机构地区：[1]商洛学院数学与计算机应用学院,陕西商洛726000 [2]陕西师范大学数学与信息科学学院,陕西西安710062

出　　处：《山东大学学报（理学版）》2016年第2期102-107,共6页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(61572016);陕西省自然科学基础研究计划项目(2013JM1023);陕西省教育厅科研计划资助项目(11JK0512)

摘　　要：以区间集思想作为研究工具,讨论非交换剩余格和滤子理论,引入区间集上非交换剩余格与区间集上非交换剩余格fuzzy滤子的概念,给出区间集上非交换剩余格〈∈,∈∪Q〉-fuzzy滤子的代数结构,进一步得到若干等价性特征刻画,并对表示定理的充分必要条件予以证明。Taking the thought of interval sets as the research tool,the theories of non-commutative residual lattices are discussed on the interval sets and filters. The concepts of non-commutative residual lattices are introduced on interval sets and fuzzy filters of non-commutative residual lattices on interval sets. The algebraic structure of the 〈∈,∈∪〉-fuzzy filters of non-commutative residual lattices is provided on interval sets,and several equivalent characterization are received. A detailed demonstration for the necessary and sufficient conditions of the representation theorem is given.

关 键 词：非可换模糊逻辑 区间集 区间集上非交换剩余格 〈∈ ∈∪〉-fuzzy滤子 特征刻画 

分 类 号：O141[理学—数学]