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Although there are many researches on the similarity measure for intuitionistic fuzzy sets, some of them have some defects. To overcome these shortcomings, based on the Euclidean distance between intuitionistic fuzzy set and three special intuitionistic fuzzy sets, a new similarity measure for intuitionistic fuzzy sets is proposed in this paper. The proposed similarity measure is compared with the existing similarity measures in intuitionistic fuzzy environment by numerical examples. Moreover, we apply the proposed similarity measure to pattern recognition problems in intuitionistic fuzzy environment. The experimental results show that the proposed similarity measure for intuitionistic fuzzy sets is reasonable and effective. [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]

Among the most classic measures in single valued neutrosophic sets (SVNS) theory, the distance is an important tool to compare and calculate degree of difference between SVNS. Although there exist some types of distance for single valued neutrosophic sets, most of them lack of strictly axiomatic definition and exist counter-intuitive cases. In this paper, a novel distance between single valued neutrosophic sets based on matrix norm is given. Then we proved that the new distance satisfies the axiomatic definition of the metric. Finally, the distance is applicated to pattern recognition and medical diagnoses. [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]