非对合剩余格的犹豫模糊理想

doi:10.6040/j.issn.1671-9352.0.2020.418

摘要/Abstract

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。

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

Abstract: 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.

Key words: fuzzy logic, logical algebra, non-involutive residuated lattice, hesitant fuzzy ideal, homomorphism

中图分类号:

O141.1

刘春辉. 非对合剩余格的犹豫模糊理想[J]. 《山东大学学报(理学版)》, 2021, 56(2): 7-16.

LIU Chun-hui. Hesitant fuzzy ideals in non-involutive residuated lattices[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(2): 7-16.

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