Multiattribute Decision Making System Based on Interval-Valued Intuitionistic Fuzzy Weights of Attributes

In this paper, we propose a new multiattribute decision making (MADM) approach in interval-valued intuitionistic fuzzy (IVIF) environments, where the attributes’ weights are represented by interval-valued intuitionistic fuzzy values (IVIFVs). First, we use the decision matrix (DM) offered by the decision maker (DK) and our proposed score function (SF) to construct a score matrix (SM). Then, a new nonlinear programming (NLP) model is developed using the hesitancy degree of each IVIFV shown in the DM, Mishra et al.’s Hellinger distance measure between interval-valued intuitionistic fuzzy sets (IVIFSs), and the IVIF weights of the attributes offered by the DK. Then, our proposed NLP model is solved to obtain the optimal weights (OPWs) of the attributes. We utilize the obtained OPWs of attributes and the obtained SM to compute the weighted scores of alternatives, where the alternatives are ranked using the weighted scores. The existing MADM approaches have drawbacks that they get unreasonable preference order (POs) of alternatives or cannot obtain the POs of alternatives in some situations. The experimental results show that proposed MADM approach gets more reasonable POs of alternatives to overcome the drawbacks of the existing MADM approaches in IVIF environments.