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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]

In this paper, the concept of α (x, y)-interval-valued pointwise sustaining degree based on the left-continuous t-representable t-norms is put forward. And then, as a general extension based on the interval-valued pointwise sustaining degree, the interval-valued α (x, y)-full implication triple I method model, the interval-valued α (x, y)-quintuple implication principle models and the interval-valued α (x, y)-similarity measure method models are given. Moreover, the interval-valued R -type α (x, y)-fuzzy reasoning solutions with triple I method, quintuple implication principle and similarity measure method are given. Some existing results are special cases of the main conclusions in this paper. [ABSTRACT FROM AUTHOR]