Multiattribute decision making method based on nonlinear programming model, cosine similarity measure, and novel score function of interval-valued intuitionistic fuzzy values

In this paper, we propose a new multiattribute decision making (MADM) method based on the proposed score function (SF) of interval-valued intuitionistic fuzzy values (IVIFVs), the cosine similarity measure of IVIFVs, and the proposed nonlinear programming (NLP) model. The proposed SF of IVIFVs overcomes some shortcomings of the existing SFs of IVIFVs. The proposed MADM method overcomes some shortcomings of the existing MADM methods based on IVIFVs. Firstly, we propose a novel SF of IVIFVs to overcome the shortcomings of some existing SFs of IVIFVs. Then, we construct a score matrix based on the proposed score function of IVIFVs and the decision matrix given by the decision maker. Then, we build a NLP model based on the cosine similarity measure of IVIFVs and the interval-valued intuitionistic fuzzy weights of the attributes. Then, we solve the NLP model to obtain the optimal weights (OWs) of the attributes, respectively. Based on the obtained OWs of the attributes and the constructed score matrix, we compute the weighted scores (WSs) of the alternatives, respectively. Finally, we rank the alternatives based on the obtained WSs. The proposed MADM method provides us a very useful approach for MADM in the interval-valued intuitionistic fuzzy context.