Fuzzy multi-attribute decision making method based on new similarity measure under interval-valued neutrosophic sets

Abstract

Interval-valued neutrosophic set (IVNS) plays an important role in dealing with imprecise judgment information. For a multi-attribute decision making problem, the information of alternatives under different attributes is given in the form of interval valued neutrosophic number(IVNN). The objective of the presented paper is to develop a multiple-attribute decision making (MADM) method under interval-valued neutrosophic sets(IVNSs) using the new similarity measurement. The similarity measurement of IVNSs has always been a research hotspot. A new similarity measurement of IVNSs is first proposed in this paper based on Chebyshev distance. The proposed method enriches the existing similarity measurement methods. It can be applied to not only IVNSs, but also single-valued neutrosophic sets(SVNSs). The influence of each attribute on the decision-making result can be described by the weight. How to formulate the weight scientifically is vital as well. In this paper, the objective weight is calculated by normalizing the grey correlation coefficient obtained by a score function which can be applied to IVNSs. The objective weight is then combined with the subjective one by considering an adjustment factor with the weighted summation method. The adjustment factor is determined by the importance of subjective weight. Finally, an example is used to illustrate the comparison results of the proposed algorithm and other three ones. The comparison shows that the proposed algorithm is effective and can identify the optimal scheme quickly.