Multiattribute decision making based on nonlinear programming methodology, novel score function of interval-valued intuitionistic fuzzy values, and the standard deviations of the score values in the score matrix

Abstract

In this paper, we propose a new multiattribute decision making (MADM) method using the proposed nonlinear programming (NLP) model, the proposed score function (SCF) of interval-valued intuitionistic fuzzy values (IVIFVs), and the standard deviation of the score values appeared in each column of the constructed score matrix (SX). The proposed SCF of IVIFVs can overcome the shortcomings of the existing SCFs of IVIFVs. Firstly, we construct the SX using the decision matrix given by the decision maker and the proposed SCF of IVIFVs. Then, we construct a NLP model using the obtained SX, the standard deviation of the score values appeared in each column of the SX, the interval-valued intuitionistic fuzzy weights of the attributes, the largest ranges of IVIFVs, and the concept of deviation variables. Then, we solve the NLP model to get the optimal weights of the attributes, respectively. Then, based on the constructed SX and the obtained optimal weights of the attributes, we calculate the weighted score of each alternative. Finally, we rank the alternatives according to the obtained weighted scores. The proposed MADM method can overcome the drawbacks of the existing MADM methods.