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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]

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, we focus on parametric interval-valued full implication algorithms. The interval-valued full implication algorithms based on a class of interval-valued t-norms with parameters are proposed. Meanwhile, the [ a , b ] -type interval-valued full implication algorithms based on a class of interval-valued t-norms with parameters are introduced. Furthermore, the solutions of these algorithms are given. Finally, the proposed algorithms are applied to pattern recognition. [ABSTRACT FROM AUTHOR]

In this paper, we focus on studying picture fuzzy reasoning full implication methods. First, picture associated t -norm and its residuated implication operator are given. Then, picture fuzzy reasoning full implication principles and the solutions of picture fuzzy reasoning full implication methods based on picture associated t -norm are given. Moreover, the reducibility and robustness of picture fuzzy reasoning full implication methods based on picture associated t -norm are proved. Finally, pattern recognition problems can be successfully solved by the proposed method. [ABSTRACT FROM AUTHOR]

The picture fuzzy set is a generation of an intuitionistic fuzzy set. The aggregation operators are important tools in the process of information aggregation. Some aggregation operators for picture fuzzy sets have been proposed in previous papers, but some of them are defective for picture fuzzy multi-attribute decision making. In this paper, we introduce a transformation method for a picture fuzzy number and trapezoidal fuzzy number. Based on this method, we proposed a picture fuzzy multiplication operation and a picture fuzzy power operation. Moreover, we develop the picture fuzzy weighted geometric ( P F W G ) aggregation operator, the picture fuzzy ordered weighted geometric ( P F O W G ) aggregation operator and the picture fuzzy hybrid geometric ( P F H G ) aggregation operator. The related properties are also studied. Finally, we apply the proposed aggregation operators to multi-attribute decision making and pattern recognition. [ABSTRACT FROM AUTHOR]

Picture fuzzy set is a generalization of intuitionistic fuzzy set, which can describe fuzzy, uncertain, incomplete and inconsistent information. Similarity measure is a technique used to evaluate the degree of similarity between picture fuzzy sets. Although there are some similarity measures between picture fuzzy sets, some of them cannot meet the axiomatic definition of similarity measure, or there are some unreasonable situations when distinguishing different picture fuzzy information. In order to overcome these defects, a new similarity measure based on the three constituent functions of picture fuzzy sets is proposed in this paper. Through a numerical example and some pattern recognition experiments, the effectiveness and superiority of the proposed similarity measure are verified. [ABSTRACT FROM AUTHOR]

In this paper, a novel similarity measure for interval-valued intuitionistic fuzzy sets is introduced, which is based on the transformed interval-valued intuitionistic triangle fuzzy numbers. Its superiority is shown by comparing the proposed similarity measure with some existing similarity measures by some numerical examples. Furthermore, the proposed similarity measure is applied to deal with pattern recognition and medical diagnosis problems. [ABSTRACT FROM AUTHOR]