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《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (9): 36-42.doi: 10.6040/j.issn.1671-9352.0.2018.560

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基于重叠函数和分组函数的蕴涵分配性

张廷海,覃锋   

  1. 江西师范大学数学与信息科学学院, 江西 南昌 330022
  • 出版日期:2019-09-20 发布日期:2019-07-30
  • 作者简介:张廷海(1974— ),男,硕士,副教授,研究方向为模糊系统与控制. E-mail:tinghaizh@163.com
  • 基金资助:
    国家自然科学基金资助项目(61563020);江西省自然科学重点基金资助项目(20171ACB20010);江西省教育厅自然科学基金资助项目(60296)

Distributivity of fuzzy implications over additively generated overlap and grouping functions

ZHANG Ting-hai, QIN Feng   

  1. College of Mathematics and Informatics, Jiangxi Normal University, Nanchang 330022, Jiangxi, China
  • Online:2019-09-20 Published:2019-07-30

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摘要： 在模糊系统中,模糊蕴涵与某些特定的聚合函数(如三角模、三角余模、一致模、零模、半一致模、半t-算子等)间的分配性被广泛研究。作为两类特殊的聚合函数,重叠函数和分组函数因其在图像处理、分类和决策等方面的应用而被广泛关注。本文给出了有加法生成子对的重叠函数、分组函数与具有边界条件的二元函数满足蕴涵分配性方程I(O(x,y),z)=G(I(x,z),I(y,z))的充要条件,以及有加法生成子对的分组函数G1,G2和具有边界条件的二元函数I满足蕴涵分配性方程I(x,G1(y,z))=G2(I(x,y),I(x,z))的充要条件。

关键词: 模糊蕴涵, 重叠函数, 分组函数, 柯西函数方程, 分配性

Abstract: Among the researches of the fuzzy system, the distributivity between fuzzy implications and some special aggregation functions(e.g. t-norms, t-conorms, uninorms, t-operators, semi-uninorms and semi-t-operators)has been studied by many authors. Overlap functions and grouping functions have been followed with interest for their applications in image processing, classification problems and decision making based on fuzzy preference relations. In this paper, we give necessary and sufficient conditions for two distributivity equations I(O(x,y),z)=G(I(x,z),I(y,z)) and I(x,G1(y,z))=G2(I(x,y),I(x,z)), where O is an additively generated overlap function, G1 and G2 are additively generated grouping functions and I is a binary function satisfying boundary conditions.

Key words: fuzzy implication, overlap function, grouping function, Cauchy function equation, distributivity

中图分类号: 

  • O159
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