MAGDM approach using the hyperbolic sine similarity measure of confidence neutrosophic number credibility sets in a fuzzy credibility multi-valued circumstance

Abstract

Group decision-making is that individuals collectively make a choice from a set of alternatives. Then, in complex decision-making problems, the decision-making process is no longer subject to a single individual, but group decision-making. Hence, the decision reliability and credibility of the collective evaluation information become more critical. However, current decision-making methods lack the confidence level and credibility measure of group evaluation information. To ensure the confidence level and credibility measure of small-scale group decision-making problems, the aim of this paper is to propose a Multi-Attribute Group Decision-Making (MAGDM) approach using a hyperbolic sine similarity measure between Confidence Neutrosophic Number Credibility Sets (CNNCSs) in the circumstance of Fuzzy Credibility Multi-Valued Sets (FCMVSs). To achieve this aim, this paper contains the following works. First, we present FCMVS to represent the mixed information of fuzzy sequences and credibility degree sequences with different and/or identical fuzzy values. Second, according to the normal distribution and confidence level of fuzzy values and credibility degrees in FCMVS, FCMVS is transformed into CNNCS to avoid the operational issue between different fuzzy sequence lengths in FCMVSs and to ensure the confidence neutrosophic numbers/confidence intervals of fuzzy values and credibility degrees. Third, a hyperbolic sine similarity measure of CNNCSs is established in the circumstance of FCMVSs. Fourth, a MAGDM approach is developed based on the weighted hyperbolic sine similarity measure in the circumstance of FCMVSs. Fifth, the proposed MAGDM approach is applied to an actual example of the equipment supplier choice problem to illustrate the efficiency and rationality of the proposed MAGDM approach in a FCMVS circumstance. In general, this study reveals new contributions in the representation, transformation method, and similarity measure of small-scale group assessment information, as well as the proposed MAGDM method subject to the normal distribution and confidence levels in small-scale MAGDM scenarios.