An interval-valued intuitionistic fuzzy LINMAP method with inclusion comparison possibilities and hybrid averaging operations for multiple criteria group decision making

An interval-valued intuitionistic fuzzy set contains membership and non-membership values that are crisp intervals and represent an extension of the ordinary fuzzy sets that are widely used because of their usefulness in handling imprecise or uncertain information. The linear programming technique for multidimensional analysis of preference (LINMAP) is a representative decision-making method with respect to preference information for given alternatives. In this paper, we present a new linear programming technique with weight assessment, an extended LINMAP method, for addressing multiple criteria group decision-making problems in the interval-valued intuitionistic fuzzy framework. With consideration given to the degrees of relative agreement and the importance weights of multiple decision makers, this paper presents an inclusion-based hybrid averaging operation with an inclusion comparison approach for forming a collective decision environment. The concept of inclusion-based indices that relate to anchor dependency with multiple points of reference is developed as the core of the extended LINMAP method. We also establish a linear programming model to handle the incomplete preference information for alternatives. The optimal weights of the criteria can be determined, and the priority order of the alternatives can be obtained according to the resulting comprehensive inclusion-based indices. The feasibility and applicability of the proposed methods are illustrated with an example addressing graduate admission, and a comparative analysis is performed with another interval-valued intuitionistic fuzzy LINMAP approach to validate the effectiveness of the proposed methodology.