L-模糊素理想度及其诱导的凸结构  

The L-fuzzy Prime Ideal Degrees and Its Induced Convexity

作　　者：安英英 王岚 左嘉昱 AN Ying-ying;WANG Lan;ZUO Jia-yu(School of Mathematical Science,Mudanjiang Normal University,Mudanjiang 157011,China)

机构地区：[1]牡丹江师范学院数学科学学院,黑龙江牡丹江157011

出　　处：《模糊系统与数学》2021年第6期123-133,共11页Fuzzy Systems and Mathematics

基　　金：黑龙江省教育厅科研备案重点项目(1354ZD009);国家自然科学基金资助项目(11371002);黑龙江省省属本科高校中央支持地方高校改革发展资金(优秀青年人才项目)(2020YQ07);中央财政支持地方高校发展专项资金优秀青年人才支持项目(ZYQN2019071);牡丹江师范学院科技创新项目(kjcx2020-15mdjnu)。

摘　　要：本文在L是完全分配格时,首先提出了L-模糊素理想度,并利用L-模糊集的四种截集对其进行了等价刻画,其次研究了由L-模糊素理想度诱导的L-模糊凸结构,同时讨论了任意多个L-模糊子集交的L-模糊素理想度以及在同态映射下象与原象的L-模糊素理想度的性质。In this paper,when L is a completely distributive lattice,Firstly,the L-fuzzy prime ideal degrees is proposed,and it is equivalently characterized by four cut sets of L-fuzzy sets.Secondly,the L-fuzzy convexity induced by L-fuzzy prime ideal degrees is studied.At the same time,the L-fuzzy prime ideal degrees of any number of L-fuzzy subsets intersection and the L-fuzzy prime principle of image and primitive image under homomorphic mapping are discussed the properties of the degree of thought.

关 键 词：完全分配格 L-模糊素理想度 L-模糊凸结构 L-模糊凸保持映射 L-模糊凸到凸映射 

分 类 号：O159[理学—数学]