基于三角模的直觉相似度及其应用

doi:10.6040/j.issn.1671-9352.0.2021.335

摘要/Abstract

摘要： 为了将直觉模糊集的相似度分析纳入到逻辑推理的框架之中,借助三角模和蕴涵算子以不同的方式构造了两种直觉模糊集的相似度,并证明了其满足相似度的四条公理。作为应用,首先以所构造的相似度为衡量指标解决了一个关于伤寒病症的医疗诊断问题,经过数据分析,得到了与直观吻合的结果。其次,以所构造的相似度为扰动参数,分析了逻辑连接词直觉三角模和直觉蕴涵的鲁棒性,进而对直觉模糊取式问题的全蕴涵推理方法和推理合成规则方法进行了鲁棒性估计,结果表明当输入的扰动非常小时,输出的结果变化也很小,两种推理方法均具有良好的鲁棒性。

关键词: 直觉模糊集, 相似度, 三角模, 鲁棒性分析

Abstract: In order to incorporate the similarity analysis of intuitionistic fuzzy sets into the framework of logical reasoning, the two similarities of intuitionistic fuzzy sets based on triangular norm and implication operator are constructed in different ways and proved that they satisfy the four axioms of similarity. As an application, firstly, a medical diagnosis problem about typhoid fever is solved by using the constructed similarity as a measurement, and the result consistent with the intuition by using data analysis. Secondly, the robustness of logical connectives, intuitionistic triangular norm and intuitionistic implication, are analyzed by using the constructed similarity as the disturbance parameter. Furthermore, the robustness of the full implication inference method and the compositional rule of inference method of the intuitionistic fuzzy modus ponens problem are analyzed. The results show that when the input disturbance is very small, the output result changes very little. Both inference methods have good robustness.

Key words: intuitionistic fuzzy set, similarity, triangular norm, robustness analysis

中图分类号:

O159

李星宇,段景瑶. 基于三角模的直觉相似度及其应用[J]. 《山东大学学报(理学版)》, 2022, 57(4): 37-47.

LI Xing-yu, DUAN Jing-yao. Intuitionistic similarity based on triangular norms and its application[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(4): 37-47.

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