基于相似度的直觉模糊推理反向三I算法的鲁棒性

doi:10.3969/j.issn.0372-2112.2020.02.006

电子学报 ›› 2020, Vol. 48 ›› Issue (2): 265-271.DOI: 10.3969/j.issn.0372-2112.2020.02.006

基于相似度的直觉模糊推理反向三I算法的鲁棒性

井美, 惠小静, 王蓉

延安大学数学与计算机科学学院, 陕西延安 716000

收稿日期:2019-03-22 修回日期:2019-09-08 出版日期:2020-02-25
- 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 Intuitionistic Fuzzy Inference Reverse Triple I Methods Based on Similarity

JING-mei, HUI Xiao-jing, WANG-rong

College of Mathematics and Computer Science, Yan'an University, Yan'an, Shaanxi 716000, China

Received:2019-03-22 Revised:2019-09-08 Online:2020-02-25 Published:2020-02-25

摘要/Abstract

摘要： 本文将直觉模糊集与反向三I算法结合起来，研究了直觉模糊推理a－反向三I算法，给出了IFMP、IFMT问题的直觉模糊推理a－反向三I算法解的表达形式和分解形式.其次，借助双剩余，定义了直觉模糊集间的相似度，给出了直觉?ukasiewicz蕴涵、直觉Gödel蕴涵、直觉Goguen蕴涵、直觉R₀蕴涵的相似度，并分析了它们之间的关系.最后，利用直觉模糊集上的相似度作为扰动参数，讨论了直觉模糊推理a－反向三I算法的鲁棒性，特别是，针对以上四种剩余型蕴涵算子，得到了直觉模糊推理a－反向三I算法的一些关于鲁棒性的结论.

关键词: 直觉模糊推理, 反向三I算法, 相似度, 鲁棒性

Abstract: We combine reverse triple I methods with intuitionistic fuzzy set, and investigate intuitionistic fuzzy inference a－ reverse triple I methods.The expression form and decomposition form of solutions of intuitionistic fuzzy inference a－ reverse triple I methods based on IFMP and IFMT problems are given.Then, similarity between intuitionistic fuzzy sets are defined by biresiduum, the similarity of intuitionistic ?ukasiewicz implication, intuitionistic Gödel implication, intuitionistic Goguen implication, intuitionistic R_o implication are provided, furthermore, their relationship are analysed.Finally, taking similarity on intuitionistic fuzzy sets as perturbation parameters, robustness of intuitionistic fuzzy inferencea－reverse triple I methods are discussed, in particular, for four kinds of residual implications, some results concerning robustness of intuitionistic fuzzy inference a－ reverse triple I methods are obtained.

Key words: intuitionistic fuzzy inference, reverse triple I methods, similarity, robustness

中图分类号:

O142

井美, 惠小静, 王蓉. 基于相似度的直觉模糊推理反向三I算法的鲁棒性[J]. 电子学报, 2020, 48(2): 265-271.

JING-mei, HUI Xiao-jing, WANG-rong. Robustness of Intuitionistic Fuzzy Inference Reverse Triple I Methods Based on Similarity[J]. Acta Electronica Sinica, 2020, 48(2): 265-271.

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基于相似度的直觉模糊推理反向三I算法的鲁棒性

Robustness of Intuitionistic Fuzzy Inference Reverse Triple I Methods Based on Similarity

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