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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2016, Vol. 33 ›› Issue (4): 391-401.doi: 10.3969/j.issn.1005-3085.2016.04.006

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有界Heyting代数的模糊$LI$-理想

刘春辉   

  1. 赤峰学院数学与统计学院，内蒙古 赤峰 024000
  • 收稿日期:2014-11-25 接受日期:2016-04-18 出版日期:2016-08-15 发布日期:2016-10-15
  • 基金资助:
    内蒙古自治区高等学校科学研究项目 (NJSY14283).

Fuzzy $LI$-ideals in Bounded Heyting Algebras

LIU Chun-hui   

  1. Department of Mathematics and Statistics, Chifeng University, Chifeng, Inner Mongolia 024000
  • Received:2014-11-25 Accepted:2016-04-18 Online:2016-08-15 Published:2016-10-15
  • Supported by:
    The Higher School Science Research Foundation of Inner Mongolia (NJSY14283).

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摘要： 理想是研究逻辑代数结构特征的重要工具性概念之一．本文综合运用代数学与模糊集的方法和原理，在有界Heyting代数中引入模糊$LI$-理想概念并研究其性质．进而讨论了模糊$LI$-理想与模糊格理想之间的关系，并给出了由一个模糊集生成的模糊$LI$-理想的表示定理，最后证明了一个给定有界Heyting代数的全体模糊$LI$-理想之集在模糊集合包含序下构成一个完备Heyting代数．

关键词: 直觉逻辑, Heyting代数, 模糊$LI$-理想, 完备Heyting代数

Abstract:

Ideals is one of the important tools for studying the structure characteristics of logical algebras. In this paper, by using methods and principles of algebra and fuzzy sets, we introduce the notion of fuzzy $LI$-ideals and investigate their properties in bounded Heyting algebras. Relation between fuzzy $LI$-ideals and fuzzy lattice ideals is also discussed. Representation theorem of fuzzy $LI$-ideal generated by a fuzzy set is provided. Furthermore, we prove that the set consisting of all fuzzy $LI$-ideals in a given bounded Heyting algebra, under fuzzy set-inclusion order, forms a complete Heyting algebra.

Key words: intuitionistic logic, Heyting algebra, fuzzy $LI$-ideal, complete Heyting algebra

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