A Method for Multi-Attribute Group Decision Making Based on Generalized Interval-Valued Intuitionistic Fuzzy Choquet Integral Operators

As an extension of the classical averaging operators, Choquet integral has been shown a powerful tool for decision theory. In this paper, a method based on the generalized interval-valued intuitionistic fuzzy Choquet integrals w.r.t. the generalized interaction indices is proposed for multi attribute group decision making problems, where the importance of the elements is considered, and their interactions are reflected. Based on the given operational laws on interval-valued intuitionistic fuzzy sets, the interval-valued intuitionistic fuzzy Choquet integrals with respect to the generalized Shapley and Banzhaf indices are defined. Moreover, some of their properties are studied, such as idempotency, boundary, comonotonic linearity and mu-linearity. Furthermore, a decision procedure based on the proposed operators is developed for solving multi-attribute group decision making under interval-valued intuitionistic fuzzy environment. Finally, a numerical example is provided to illustrate the developed procedure.