Possibility degree and divergence degree based method for interval-valued intuitionistic fuzzy multi-attribute group decision making

Abstract

This paper investigates an order relation of interval-valued intuitionistic fuzzy values (IVIFVs) based on possibility degree and divergence degree and applies it to multi-attribute group decision making (MAGDM) problems. Firstly, based on the possibility degree of intuitionistic fuzzy values, the possibility degree and divergence degree of IVIFVs are defined to provide a new order relation of IVIFVs. Subsequently in interval-valued intuitionistic fuzzy MAGDM, an intuitionistic fuzzy linear programming model is constructed to derive decision makers' weights. Depending on the construction of membership and non-membership functions, three approaches are developed to solve the constructed intuitionistic fuzzy linear programming model, including the optimistic, pessimistic and mixed approaches. Utilizing decision makers’ weights, the collective decision matrix is obtained. Combining the possibility and divergence degrees of alternatives on attributes, the adjusted possibility distribution matrix for each attribute is constructed and proved to be an interval fuzzy preference relation. Then the attribute weights are determined by the negative distances and the positive distances of adjusted possibility distribution matrices. Using the interval-valued intuitionistic weighted arithmetic aggregation operator, the collective comprehensive values of alternatives are obtained. The ranking order of alternatives is generated according to the proposed order relation of IVIFVs. Therefore, an interval-valued intuitionistic fuzzy MAGDM method is proposed. Finally, the proposed method is implemented on some examples. Validation discussion and comparative analyses of this method is also done to show the effectiveness of the proposed method.