MAGDM Model Using the Exponential Similarity Measure of Neutrosophic Confidence Cubic Sets in a Single-Valued Neutrosophic Multivalued Circumstance

Abstract

Probability estimation of small sample data is a key tool to ensure the probability that sample data fall within the confidence interval at a certain confidence level and probability distribution, which shows its advantages in practical engineering applications. Then, regarding a group decision-making (GDM) problem in the situation of indeterminacy and inconsistency, several experts/decision makers will assign several true, false, and indeterminate fuzzy values to the evaluation values of each alternative over different attributes, and then form a single-valued neutrosophic multivalued set (SvNMVS) as their assessed information. To ensure some confidence level of the evaluation values in the circumstance of SvNMVSs and GDM reliability, this paper aims to propose a conversion technique from SvNMVS to a neutrosophic confidence cubic set (NCCS) and a GDM model using the exponential similarity measure of NCCSs in the circumstance of SvNMVSs. First, we give the definition of NCCS, which is transformed from SvNMVS in terms of average values and confidence intervals of true, false, and indeterminate fuzzy sequences subject to the conditions of the normal distribution and confidence levels. Second, we present the exponential similarity measure of NCCSs and the weighted exponential similarity measure of NCCSs and their characteristics. Third, a GDM model is developed by using the weighted exponential similarity measure of NCCSs in the circumstance of SvNMVSs. Fourth, the developed GDM model is applied to a choice case of landslide treatment schemes in the circumstance of SvNMVSs to reveal its usability and suitability in actual GDM problems. Compared with the existing GDM models, the developed GDM model indicates its superiorities in decision flexibility and credibility/reliability subject to 90%, 95%, and 99% confidence levels.