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

Abstract

This paper proposes a new multiple attribute decision making (MADM) method based on the proposed score function (SF) of interval-valued intuitionistic fuzzy values (IVIFVs), the score matrix (SMT), and the proposed nonlinear programming model. Firstly, we use the proposed SF of IVIFVs to construct the SMT, where the proposed SF of IVIFVs can overcome the drawbacks of the existing SFs of IVIFVs. Then, we calculate the average value of the values appeared at each column of the SMT. Then, we construct the nonlinear programming model using the obtained SMT, the obtained average value of the values appeared at each column of the SMT, the concept of deviation variables, and the interval-valued intuitionistic fuzzy weight of each attribute offered by the decision maker. Then, we solve the nonlinear programming model to obtain the optimal weight (OW) of each attribute. Then, we calculate the weighted score (WTS) of each alternative using the obtained SMT and the OWs of the attributes. Finally, we rank the alternatives according to the obtained WTSs. The bigger the WTS of an alternative, the better the preference order (PO) of the alternative. Our proposed MADM method can overcome the shortcomings of the existing MADM methods.