JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2022, Vol. 57 ›› Issue (4): 37-47.doi: 10.6040/j.issn.1671-9352.0.2021.335

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Intuitionistic similarity based on triangular norms and its application

LI Xing-yu, DUAN Jing-yao*   

  1. School of Mathematics and Information Science, Baoji University of Arts and Sciences, Baoji 721013, Shaanxi, China
  • Published:2022-03-29

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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

CLC Number: 

  • O159
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