An Interval-Valued Best–Worst Method with Normal Distribution for Multi-criteria Decision-Making

Abstract

A novel three-stage multi-criteria decision-making (MCDM) method considering the interval-valued best–worst method (BWM) and social networks including the following three main modules is put forward: (1) the weights of experts; (2) the weights of criteria; (3) the weighted sum method (WSM). Firstly, a new framework for computing the weights of experts in social networks is construct. Let the values of trust and distrust be interval values rather than fixed values, and then construct a complete trust preference matrix through trust propagation. Subsequently, trust score obtained by synthesizing the trust preference matrix is used to assign the weights of experts. Secondly, an interval-valued BWM model with normal distribution is developed to compute the weights of criteria. The proposed BWM model innovatively uses interval fuzzy numbers with normal distribution to represent the preference degree of experts instead of the fixed values in the basic BWM model. Thirdly, considering the WSM, this paper constructs a novel three-stage MCDM method considering the proposed novel BWM model and social networks. The proposed MCDM model innovatively aims at the situation where both the weights of experts and criteria are not known, and provides mathematical models for solving them respectively. Finally, a case is used to prove the utility and availability of the novel MCDM method. The results show that the novel MCDM method can not only reduce the subjectivity in decision making, but also can effectively solve the MCDM problems.