刘春辉.非对合剩余格的正规双极值模糊理想[J].数学研究及应用,2020,40(5):441~452
非对合剩余格的正规双极值模糊理想
Normal Bipolar Fuzzy Ideals in Non-involutive Residuated Lattices
投稿时间:2019-08-20  修订日期:2020-03-19
DOI:10.3770/j.issn:2095-2651.2020.05.001
中文关键词:  非经典逻辑  非对合剩余格  双极值模糊集  正规双极值模糊理想
英文关键词:non-classical logic  non-involutive residuated lattice  bipolar fuzzy set  normal bipolar fuzzy ideal
基金项目:内蒙古自治区高等学校科学研究项目(Grant No.NJZY18206).
作者单位
刘春辉 赤峰学院数学与与计算机科学学院, 内蒙古 赤峰 024001 
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中文摘要:
      本文对非对合剩余格的双极值模糊理想问题作进一步深入研究.引入了非对合剩余格的正规双极值模糊理想概念, 考察了其性质并获得了其若干等价刻画.同时, 给出了两类特殊的双极值模糊理想的定义, 分别称为极大双极值模糊理想和完全正规双极值模糊理想并讨论了它们的性质和相互关系.这些工作为进一步揭示非对合剩余格的结构特征拓展了研究思路.
英文摘要:
      In this paper, the problem of bipolar fuzzy ideal is further studied in non-involutive residuated lattices. The notion of normal bipolar fuzzy ideal is introduced, some important properties and equivalent characterizations of normal bipolar fuzzy ideals are obtained. In addition, two special types of normal bipolar fuzzy ideals are defined, which are called maxima and completely normal bipolar fuzzy ideals, respectively, and their relationships are discussed. This work further expands the way for revealing the structural characteristics of non-involutive residuated lattices.
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