非对合剩余格的BF-MV理想  

BF-MV-ideals in Non-involutive Residuated Lattices

作　　者：刘春辉 LIU Chunhui(Education Science College,Chifeng University,Chifeng 024000,Inner Mongolia)

机构地区：[1]赤峰学院教育科学学院,内蒙古赤峰024000

出　　处：《四川师范大学学报(自然科学版)》2025年第4期558-568,共11页Journal of Sichuan Normal University(Natural Science)

基　　金：内蒙古自治区高等学校科学研究项目(NJZY21138和NJZY22146);赤峰学院教育教学研究项目(JYJXZ202204)。

摘　　要：深入研究非对合剩余格的双极值模糊理想(简称BF-理想)问题.首先,引入非对合剩余格的BF-MV理想的概念,获得BF-MV理想的若干性质和等价刻画.其次,讨论BF-MV理想与其他类型的BF-理想概念间的相互关系.最后,利用BF-MV理想的性质给出对合剩余格成为MV代数的刻画定理.In this paper,the problem of bipolar fuzzy ideals(BF-ideals for short)in non-involutive residuated lattices is studied in deepth.Firstly,the notion of BF-MV-ideals is introduced in non-involutive residuated lattices and some of its properties and characterizations are obtained.Secondly,the relationships among BF-MV-ideals and other type BFideals are discussed.Finally,the characterization theorem of an involutive residuated lattice forms a MV-algebra is given by using the properties of BF-MV-ideals.

关 键 词：模糊逻辑 非对合剩余格 BF-理想 BF-MV理想 MV代数 

分 类 号：O141.1[理学—数学] O153.1[理学—基础数学]