Multiattribute Decision Making Based on Nonlinear Programming Methodology, the Euclidean Distance Between IVIFVs, and New Score Function of IVIFVs

In this paper, we propose a new multiattribute decision making (MADM) method based on the proposed nonlinear programming methodology, the Euclidean distance between interval-valued intuitionistic fuzzy values (IVIFVs), and the proposed score function of IVIFVs. Firstly, a new score function of IVIFVs is proposed to overcome the shortcomings of the existing score functions of IVIFVs. Then, we construct the score matrix based on the proposed score function of IVIFVs and the decision matrix given by the decision maker. Then, a nonlinear programming model is proposed based on the Euclidean distance between IVIFVs and the interval-valued intuitionistic fuzzy weights of the attributes provided by the decision maker. Then, we solve the proposed nonlinear programming model to obtain the optimal weights of the attributes. Then, the weighted score of each alternative is calculated based on the obtained score matrix and the obtained optimal weights of the attributes. Finally, the alternatives are ranked according to the obtained weighted scores of the alternatives. The MADM method proposed in this paper can conquer the shortcomings of the existing MADM methods in the environments of IVIFVs.