Multiple attribute decision making based on novel nonlinear programming model, the distance between score values, and novel score function of interval-valued intuitionistic fuzzy values

Abstract

In this paper, we propose a novel multiple attribute decision making (MADM) method based on the proposed nonlinear programming (NLP) model, the distance between the score values appeared in the constructed score matrix (SCMX), and the proposed score function (SF) of interval-valued intuitionistic fuzzy values (IVIFVs), where the NLP model is used to get the optimal weights (OWs) of the attributes. Firstly, we propose a novel SF to conquer the shortcomings of the existing SFs of IVIFVs. Then, we use the proposed SF to construct the SCMX from the decision matrix (DM) given by the decision maker (DK). Then, we propose a NLP model to obtain the OWs of the attributes based on the distance between the score values appeared in the constructed SCMX, the interval-valued intuitionistic fuzzy weights (IVIFWs) of the attributes provided by the DK, the concept of deviation variables, and the largest range of the IVIFW of each attribute. Then, we calculate the weighted score (WS) of each alternative based on the obtained SCMX and the obtained OWs of the attributes. Finally, we rank the alternatives according to the WSs of the alternatives. The proposed MADM method can conquer the shortcomings of the existing MADM methods.