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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 ›› 2021, Vol. 38 ›› Issue (6): 822-844.doi: 10.3969/j.issn.1005-3085.2021.06.006

• • 上一篇    下一篇

基于连续三角模方幂的模糊蕴涵关于三角模与三角余模的分配方程

付伊嘉,   周红军   

  1. 陕西师范大学数学与统计学院，西安 710119
  • 出版日期:2021-12-15 发布日期:2022-02-15
  • 通讯作者: 周红军 E-mail: hjzhou@snnu.edu.cn
  • 基金资助:
    国家自然科学基金 (61473336; 12171292)；陕西省青年科技新星计划 (2016KJXX-24).

Distributivity of T-power Implications Over t-norms and t-conorms

FU Yijia,   ZHOU Hongjun   

  1. School of Mathematics and Statistics, Shaanxi Normal University, Xi'an 710119
  • Online:2021-12-15 Published:2022-02-15
  • Contact: H. Zhou. E-mail address: hjzhou@snnu.edu.cn
  • Supported by:
    The National Natural Science Foundation of China (61473336; 12171292); the Youth Science and Technology Star Program of Shaanxi Province (2016KJXX-24).

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185

摘要：

模糊蕴涵关于三角模和三角余模的分配方程在近似推理，特别是在模糊推理与控制中起着重要作用，此类分配方程已得到大量研究并取得丰硕成果。最近，Massanet 等基于连续三角模的方幂提出了一类新的模糊蕴涵，简称 T-幂蕴涵，并且对它的基本性质做了深入研究。为拓展 T-幂蕴涵以及各类模糊蕴涵关于三角模和三角余模分配方程的知识体系，通过分类讨论法，分别研究了三类 T-幂蕴涵关于一般三角模与三角余模的四个分配方程，给出 T- 幂蕴涵关于三角模和三角余模的四个分配方程成立的充要条件。最后通过反证法推导出 T-幂蕴涵不同于其他各类已知模糊蕴涵，完善了模糊蕴涵的知识框架。

关键词: 模糊蕴涵, T-幂蕴涵, 分配方程, 三角模, 三角余模

Abstract:

Distributivity equations of fuzzy implications over triangular norms and triangular conorms play an important role in approximate reasoning, especially in fuzzy reasoning and control. A great deal of researches have been done on the distributivity equations of fuzzy implications over triangular norms and triangular conorms. Recently, Massanet et al. proposed a new kind of fuzzy implications based on powers of continuous t-norms, called T-power based implications and made an in-depth study of its properties. To extend the knowledge system of T-power implications and distributivity equations of fuzzy implications over triangular norms and triangular conorms, the paper studies four distributivity equations of T-power implications over triangular norms and triangular conorms. Necessary and sufficient conditions for the four distributivity equations of T-power implications over triangular norms and triangular conorms are given. This paper also points out that T-power implications are different from other well-known classes of fuzzy implications, and improves finally the knowledge framework of fuzzy implications.

Key words: fuzzy implication, T-power implication, distributivity equations, t-norm, t-conorm

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