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As the theory of picture fuzzy sets has been developed, more information in life can be expressed in mathematical terms. Similarity measure is a special tool for quantifying the similarity between two sets, so studying similarity measure on picture fuzzy sets has become a trending topic. This new research direction has drawn a great deal of attention from experts and has led to a number of important results which have led to significant results in a number of practical applications. By examining these new findings, we discovered that there are many studies on similarity measure of picture fuzzy sets, some of them are deficient in solving certain problems, and such similarity measures can lead to the calculation of unreasonable data in practical applications, affecting the final results. Secondly, there is still room for research similarity measures on exponential functions. Considering these two aspects, we propose two new similarity measures based on exponential function, which not only satisfy the axiomatic definition of similarity measures, but also show reasonable computational results in practical applications. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]