A Novel Single Valued Neutrosophic Set Similarity Measure And Its Application In Multicriteria Decision Making

The single-valued neutrosophic set is a subclass of neutrosophi cset, and has been proposed in recent years. An important application for single-valued neutrosophic sets is to solve multicriteria decision-making problems.

In this paper, we propose three similarity measure methods for single-valued neutrosophic refined sets and interval neutrosophic refined sets based on Jaccard, Dice and Cosine similarity measures of single-valued neutrosophic sets and interval neutrosophic sets.

The single-valued neutrosophic set is a subclass of neutrosophic set, and has been proposed in recent years. An important application for single-valued neutrosophic sets is to solve multicriteria decision-making problems.

In this paper, a definition of quadripartitioned single valued bipolar neutrosophic set (QSVBNS) is introduced as a generalization of both quadripartitioned single valued neutrosophic sets (QSVNS) and bipolar neutrosophic sets (BNS). There is an inherent symmetry in the definition of QSVBNS. Some operations on them are defined and a set theoretic study is accomplished. Various similarity measures and distance measures are defined on QSVBNS. An algorithm relating to multi-criteria decision making problem is presented based on quadripartitioned bipolar weighted similarity measure. Finally, an example is shown to verify the flexibility of the given method and the advantage of considering QSVBNS in place of fuzzy sets and bipolar fuzzy sets.

This paper introduces a refined single-valued neutrosophic set (RSVNS) and presents a similarity measure of RSVNSs. Then a multicriteria decisionmaking method with RSVNS information is developed based on the similarity measure of RSVNSs.

As the generalization of the fuzzy and similar sets based on Fuzzy sets, neutrosophic sets provide significant possibilities in the case of solving complex decision problems, often related to uncertainty and unreliability. Neutrosophic sets use three values named the truth degree, the indeterminacy degree and the falsity degree, which allow for a more accurate evaluation of alternatives in relation to complex evaluation criteria. As a result of their application in solving numerous different decision-making problems, several approaches to their ranking have been proposed. Therefore, this paper provides a comprehensive overview of the approaches to the ranking of single-valued neutrosophic numbers and a comparison of the results obtained by using them. Finally, numerical illustrations are given.

The theme of this work is to present an axiomatic definition of divergence measure for single-valued neutrosophic sets (SVNSs). The properties of the proposed divergence measure have been studied. Further, we develop a novel technique for order preference by similarity to ideal solution (TOPSIS) method for solving single-valued neutrosophic multi-criteria decision-making with incomplete weight information. Finally, a numerical example is presented to verify the proposed approach and to present its effectiveness and practicality.

The theme of this work is to present an axiomatic definition of divergence measure for single-valued neutrosophic sets (SVNSs). The properties of the proposed divergence measure have been studied. Further, we develop a novel technique for order preference by similarity to ideal solution (TOPSIS) method for solving single-valued neutrosophic multi-criteria decision-making with incomplete weight information. Finally, a numerical example is presented to verify the proposed approach and to present its effectiveness and practicality.