非对合剩余格的犹豫模糊理想  

Hesitant fuzzy ideals in non-involutive residuated lattices

作　　者：刘春辉 LIU Chun-hui(School of Mathematics and Computer Science,Chifeng University,Chifeng 024001,Inner Mongolia,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：《山东大学学报（理学版）》2021年第2期7-16,共10页Journal of Shandong University(Natural Science)

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研究非对合剩余格的理想问题。引入了非对合剩余格的犹豫模糊理想概念,给出了犹豫模糊理想的若干性质,获得了犹豫模糊理想的若干等价刻画,讨论了犹豫模糊理想与理想间的关系。证明了非对合剩余格的犹豫模糊理想的犹豫模糊交集、同态像和同态原像仍为犹豫模糊理想。同时,给出了犹豫模糊理想的犹豫模糊并集成为犹豫模糊理想的一个充分条件。为进一步揭示非对合剩余格的结构特征拓展了研究思路。In this paper, the problem of ideals in non-involutive residuated lattices is studied by using the method and principle of hesitant fuzzy sets. The notion of hesitant fuzzy ideals of non-involutive residuated lattices is introduced. Some properties of hesitant fuzzy ideals are investigated. Some equivalent characterizations of hesitant fuzzy ideals are obtained. The relation between hesitant fuzzy ideals and ideals is discussed. It is proved that the hesitant fuzzy intersection of some hesitant fuzzy ideals, homomorphism image and inverse image of a hesitant fuzzy ideal are also hesitant fuzzy ideals. At the same time, a sufficient condition which makes the hesitant fuzzy union of some hesitant fuzzy ideals to be a hesitant fuzzy ideal is given. This work further expands the way for revealing the structural characteristics of non-involutive residuated lattices.

关 键 词：模糊逻辑 逻辑代数 非对合剩余格 犹豫模糊理想 同态 

分 类 号：O141.1[理学—数学] O153.1[理学—基础数学]