电子学报 ›› 2019, Vol. 47 ›› Issue (2): 410-416.DOI: 10.3969/j.issn.0372-2112.2019.02.021

• 学术论文 • 上一篇    下一篇

基于直觉模糊推理(1,2,2)-a型泛三I算法的鲁棒性

惠小静, 井美, 王蓉   

  1. 延安大学数学与计算机科学学院, 陕西延安 716000
  • 收稿日期:2018-06-04 修回日期:2018-09-19 出版日期:2019-02-25 发布日期:2019-02-25
  • 通讯作者: 井美
  • 作者简介:惠小静 女,1973年出生于陕西榆林,教授、博士、硕士生导师.研究方向为数理逻辑与不确定性推理.E-mail:xhmxiaojing@163.com
  • 基金资助:
    国家自然科学基金(No.11471007,No.61763045)

Robustness of(1,2,2)-a Type Universal Triple I Methods Based on Intuitionistic Fuzzy Inference

HUI Xiao-jing, JING-mei, WANG-rong   

  1. College of Mathematics and Computer Science, Yan'an University, Yan'an, Shaanxi 716000, China
  • Received:2018-06-04 Revised:2018-09-19 Online:2019-02-25 Published:2019-02-25
  • Supported by:
     

摘要: 本文基于直觉模糊集,研究了直觉模糊推理(1,2,2)-a型泛三I算法,给出了IFMP、IFMT问题的直觉模糊推理(1,2,2)-a型泛三I算法解的表达形式和分解形式.其次,利用直觉模糊集间的自然距离定义了直觉模糊连接词和直觉模糊集的灵敏度,给出了直觉Lukasiewicz蕴涵、直觉Gödel蕴涵以及它们各自对应三角模的灵敏度,在此基础上,证明了直觉Lukasiewicz蕴涵是直觉模糊集上最鲁棒剩余型蕴涵算子.最后,讨论了直觉模糊推理(1,2,2)-a型泛三I算法的鲁棒性,并且针对以上两种具体蕴涵算子,相应地获得了直觉模糊推理(1,2,2)-a型泛三I算法解的灵敏度.结论表明,直觉模糊推理算法的鲁棒性完全取决所选择的直觉模糊连接词.

 

关键词: 鲁棒性, 直觉模糊推理, 泛三I算法, 解的灵敏度

Abstract: The intuitionistic fuzzy inference(1,2,2)-a type universal triple I methods based on intuitionistic fuzzy set are discussed,the expression form and decomposition form of solutions of intuitionistic fuzzy inference(1,2,2)-a type universal triple methods based on IFMP and IFMT problems are given.Then,based on the natural distances between intuitionistic fuzzy sets,the sensitivity of intuitionistic fuzzy connectives and intuitionistic fuzzy sets are defined,the sensitivity of intuitionistic Lukasiewicz implication,intuitionistic Gödel implication and their corresponding triangular norm are provided.On this basis,it is proved that intuitionistic Lukasiewicz implication is the most robust residual implication on intuitionistic fuzzy sets.Finally,robustness of intuitionistic fuzzy inference(1,2,2)-a type universal triple I methods are investigated,corresponding sensitivity of solutions of intuitionistic fuzzy inference type universal triple methods are obtained for two kinds of specific implications.These results indicated that the robustness of intuitionistic fuzzy inference methods directly depended on the selection of intuitionistic fuzzy connectives.

Key words: robustness, intuitionistic fuzzy inference, universal triple I methods, sensitivity of solutions

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