非对合剩余格的犹豫模糊理想理论  

Hesitant Fuzzy Ideals Theory of Non-involutive Residuated Lattices

作　　者：刘春辉 LIU Chun-hui(School of Mathematics and Computer Science,Chifeng University.Chifeng 024001,China)

机构地区：[1]赤峰学院数学与计算机科学学院,内蒙古赤峰024001

出　　处：《模糊系统与数学》2021年第5期15-35,共21页Fuzzy Systems and Mathematics

基　　金：内蒙古自治区高等学校科学研究项目(NJZY18206)

摘　　要：运用犹豫模糊集的方法和原理系统研究非对合剩余格的理想问题。在非对合剩余格中引入了犹豫模糊弱理想,犹豫模糊理想,犹豫模糊Glivenko理想,犹豫模糊MV理想、犹豫模糊Boolean理想、犹豫模糊关联理想,犹豫模糊正关联理想,犹豫模糊素理想和犹豫模糊超理想等多种概念,给出了它们的若干性质和等价刻画。系统讨论了各类理想概念间的相互关系,证明了:(1)在非对合剩余格中,犹豫模糊Boolean理想、犹豫模糊关联理想和犹豫模糊正关联理想等同;(2)在Glivenko代数中,犹豫模糊弱理想,犹豫模糊理想和犹豫模糊Glivenko理想等同;(3)在BL代数中,犹豫模糊Glivenko理想和犹豫模糊MV理想等同;(4)在MTL代数中,一个犹豫模糊理想是犹豫模糊超理想当且仅当它既是犹豫模糊Boolean理想又是犹豫模糊素理想。In this paper, we deeply study the problem of ideals in non-involutive residuated lattices by using the principle and method of hesitant fuzzy sets. Various notions of hesitant fuzzy ideals, hesitant fuzzy weak, Glivenko, MV, Boolean, implicative, positive implication, prime and ultra ideals are introduced in non-involutive residuated lattices. Some their properties and characterizations are given. Relations among these various notions are discussed systematically. It is proved that:(1) the notions of hesitant fuzzy Boolean, implicative and positive implicative ideals coincide in non-involutive residuated lattices,(2) the notions of hesitant fuzzy ideals, hesitant fuzzy weak and Glivenko ideals coincide in Glivenko algebras,(3) the notions of hesitant fuzzy Glivenko and MV ideals coincide in BL-algebras, and(4) a hesitant fuzzy ideal is a hesitant fuzzy ultra ideal if and only if it is both a hesitant fuzzy Boolean ideal and a hesitant fuzzy prime ideal in MTL-algebras.

关 键 词：非对合剩余格 犹豫模糊理想 犹豫模糊Glivenko理想 犹豫模糊MV理想 犹豫模糊Boolean理想 犹豫模糊超理想 

分 类 号：O141[理学—数学] O153[理学—基础数学]