Search

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]

As an extension of intuitionistic fuzzy sets, picture fuzzy sets can deal with vague, uncertain, incomplete and inconsistent information. The similarity measure is an important technique to distinguish two objects. In this study, a similarity measure between picture fuzzy sets based on relationship matrix is proposed. The new similarity measure satisfies the axiomatic definition of similarity measure. It can be testified from a numerical experiment that the new similarity measure is more effective. Finally, we apply the proposed similarity measure to multiple-attribute decision making. [ABSTRACT FROM AUTHOR]

A new distance metric between interval-valued fuzzy sets is proposed. The four special logic metric spaces based on the distance are structured. we analysis and compare the structures of the four logic metric spaces. It is shown that the Łukasiewicz logic metric space and Goguen logic metric space are more suitable for interval-valued fuzzy reasoning. Moreover, the robustness of interval-valued fuzzy reasoning triple I methods are studied in the two logic metric spaces. We prove that fuzzy reasoning triple I methods based on the interval-valued Łukasiewicz residuated implication and interval-valued Goguen residuated implication are robust. [ABSTRACT FROM AUTHOR]

A new distance metric between interval-valued fuzzy sets is proposed. The four special logic metric spaces based on the distance are structured. we analysis and compare the structures of the four logic metric spaces. It is shown that the Łukasiewicz logic metric space and Goguen logic metric space are more suitable for interval-valued fuzzy reasoning. Moreover, the robustness of interval-valued fuzzy reasoning triple I methods are studied in the two logic metric spaces. We prove that fuzzy reasoning triple I methods based on the interval-valued Łukasiewicz residuated implication and interval-valued Goguen residuated implication are robust. [ABSTRACT FROM AUTHOR]

In this paper, a new tangent similarity between single valued neutrosophic sets is given, which contain tangent similarity [23] as a special case. A best-worst multi-criteria decision making method based on the single valued neutrosophic sets is proposed. To achieve this goal, we design an algorithm to identify the best and worst criteria through computing the out-degrees and in-degrees of the collective single valued neutrosophic preference relation directed network, and then calculate the optimal weight vector of attributes. Moreover, a mathematical model corresponding to the definitions of consistent single valued neutrosophic preference relation is contracted. Finaly, the evaluation values of all alternatives are calculated by the proposed new tangent similarity. This approach can make the process of decision making more vivid, intuitive and dynamic in the decision-making process. To illustrate the effectiveness of the proposed method, we used it to solve appointment registration systems problems. [ABSTRACT FROM AUTHOR]

In this paper, a new tangent similarity between single valued neutrosophic sets is given, which contain tangent similarity [23] as a special case. A best-worst multi-criteria decision making method based on the single valued neutrosophic sets is proposed. To achieve this goal, we design an algorithm to identify the best and worst criteria through computing the out-degrees and in-degrees of the collective single valued neutrosophic preference relation directed network, and then calculate the optimal weight vector of attributes. Moreover, a mathematical model corresponding to the definitions of consistent single valued neutrosophic preference relation is contracted. Finaly, the evaluation values of all alternatives are calculated by the proposed new tangent similarity. This approach can make the process of decision making more vivid, intuitive and dynamic in the decision-making process. To illustrate the effectiveness of the proposed method, we used it to solve appointment registration systems problems. [ABSTRACT FROM AUTHOR]