Relative measure-based approaches for ranking single-valued neutrosophic values and their applications

During uncertain information processing on generalized fuzzy values, how to rank two single-valued neutrosophic values is an important and omnipresent issue in all kinds of intelligent decision problems solving. Although many orders have been proposed to compare any two single-valued neutrosophic values, some shortcomings may exist when they are utilized. Inspired by the Euclidean approach for ranking intuitionistic fuzzy values, we present two types of orders by using the notion of relative geometric distance and relative similarity degree, respectively. First, we present two relative distance-based and relative similarity-based measures to describe the favorable degree of the single-valued neutrosophic value by considering three distances and similarity degrees between a single-valued neutrosophic value and the ideal negative point, ideal positive point, and most uncertain point. Second, two orders over the set of all single-valued neutrosophic values and the corresponding ranking methods for single-valued neutrosophic sets are devised on the basis of the presented measures of an single-valued neutrosophic value, and their properties are discussed. Third, we extend the presented ranking method for single-valued neutrosophic values and single-valued neutrosophic sets by introducing human attitudes using different weights. Finally, we apply the presented methods to optimal alternative selection and group decision making and obtain the effective and reasonable results. The main thoughts of this study can be applied in various generalized fuzzy decision problem solving.

Automated summary

This study focuses on ranking single-valued neutrosophic values by proposing two methods based on relative geometric distance and relative similarity degree. The approach extends the ranking method by introducing human attitudes and weights, and can be applied in various generalized fuzzy decision problem solving.