A new multiattribute decision making method based on interval-valued intuitionistic fuzzy values

The existing multiattribute decision making (MADM) methods have the drawback that they cannot distinguish the preference order of alternatives in the context of interval-valued intuitionistic fuzzy values (IVIFVs) in some situations or they cannot deal with interval-valued intuitionistic fuzzy weights. Therefore, it is necessary to develop a new MADM method to overcome the drawback of the existing MADM methods. This paper proposes a new MADM method to overcome the drawbacks of the existing MADM methods in the context of IVIFVs, where the weights of attributes given by the decision makers are represented by interval-valued intuitionistic fuzzy values. Firstly, we propose a novel score function (SCFT) of IVIFVs to overcome the drawbacks of the existing SCFTs of IVIFVs. Based on the proposed SCFT of IVIFVs and the decision matrix (DCM) provided by the decision maker (DCMR), a score matrix (SCMX) is constructed. Then, a new nonlinear programming (NLP) model is developed to obtain the optimal weights of the attributes, which are used to calculate the weighted scores of the alternatives to rank the alternatives. The proposed MADM method can overcome the shortcomings of the existing MADM methods in the environment of IVIFVs.