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《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (5): 99-111.doi: 10.6040/j.issn.1671-9352.0.2018.381

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(O,N)-蕴涵及其刻画

刘晓,周红军*   

  1. 陕西师范大学数学与信息科学学院, 陕西 西安 710119
  • 发布日期:2019-05-09
  • 作者简介:刘晓(1993— ),女,硕士研究生,研究方向为不确定性推理. E-mail:13619225818@163.com*通信作者简介:周红军(1980— ),男,教授,博士生导师,研究方向为不确定性推理. E-mail:hjzhou@snnu.edu.cn
  • 基金资助:
    国家自然科学基金资助项目(61473336);陕西省青年科技新星计划(2016KJXX-24)

(O,N)-implication and its characterizations

LIU Xiao, ZHOU Hong-jun*   

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xian, 710119, Shaanxi, China
  • Published:2019-05-09

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摘要： 模糊蕴涵在模糊集理论的理论建立和应用方面都发挥着非常重要的作用。常见的模糊蕴涵通常是由三角模、三角余模和模糊否定通过合适的方法构造而成。根据不同的构造方法,大致可以将模糊蕴涵分为5类,即(S,N)-蕴涵、R-蕴涵、QL-蕴涵、Yager蕴涵和序和蕴涵。本文从经典逻辑中的重言式p→q≡(p∧q)出发,在模糊逻辑中研究由重叠函数O和模糊否定N按上述方式生成的模糊蕴涵,称为(O,N)-蕴涵。本文研究(O,N)-蕴涵的基本性质和等价刻画,研究了由(O,N)-蕴涵和模糊否定诱导的类函数和重叠函数。

关键词: 模糊蕴涵, (O,N)-蕴涵, 重叠函数, 模糊否定

Abstract: Fuzzy implications paly an important role in both theoretic and applied communities of fuzzy set theory. The well-known fuzzy implications are usually constructed in appropriate ways from t-norms, t-conorms and fuzzy negations, and according to construction methods, they can be roughly classified into five classes, namely (S,N)-implications, R-implications, QL-implications, Yagers implications and ordinal sum implications. We introduce a new class of implications, called (O,N)-implications, generated from overlap functions O and fuzzy negations N inspired by the classical tautology p→q≡(p∧q). We discuss the properties of (O,N)-implications and give some characterizations of them. Finally, grouping functions and overlap functions generated by (O,N)-implications and fuzzy negations are investigated.

Key words: fuzzy implication, (O,N)-implication, overlap function, fuzzy negation

中图分类号: 

  • O142
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[1] 彭家寅. 剩余格上的落影模糊滤子[J]. 山东大学学报（理学版）, 2018, 53(2): 52-64.
[2] 于俊红,周红军. (T,N)-蕴涵及其基本性质[J]. 山东大学学报（理学版）, 2017, 52(11): 71-81.
[3] 郝加兴,吴洪博. 基于非交换剩余格的模糊蕴涵滤子及其性质[J]. J4, 2010, 45(10): 61-65.
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