Abstract
Similarity measure is an important tool to evaluate the degree of similarity between different objects. Therefore, a large number of similarity measures on picture fuzzy sets have been studied. However, some existing similarity measures have not been unified into a framework. The aim of this paper is to study a construction method of similarity measure on picture fuzzy sets, based on this, we can unify some existing similarity measures into a framework, and then propose some new similarity measures. Firstly, the concept of picture fuzzy equivalence is introduced. Some construction methods for picture fuzzy equivalence are given. Secondly, a construction method of similarity measure on picture fuzzy sets is proposed. Some new similarity measures on picture fuzzy sets based on picture fuzzy equivalences are given and some existing similarity measures are unified into a framework. Finally, the proposed similarity measures are applied to pattern recognition. By comparing the degrees of confidence, we find that our degrees of confidence are higher than some similarity measures. The experimental results show that the proposed similarity measures can effectively distinguish some similar picture fuzzy sets.
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This work is supported by the National Natural Science Foundation of China (No.12171445).
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Minxia Luo initiated the research and provide the framework of this paper. Wenling Li wrote and complete this paper with Minxia Luo’s validity and helpful suggeations.
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Luo, M., Li, W. Some new similarity measures on picture fuzzy sets and their applications. Soft Comput 27, 6049–6067 (2023). https://doi.org/10.1007/s00500-023-07902-w
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DOI: https://doi.org/10.1007/s00500-023-07902-w