Shapley divergence measures with VIKOR method for multi-attribute decision-making problems

Uncertainty is the most usual problem in decision making, for which intuitionistic fuzzy set (IFS) considered as appropriate means allowing numerous feasible degree of an element to a set. In this paper, we mention first dilemma of the existing divergence measures for IFSs. Next, we propose new divergence and entropy measures for IFSs and compare with the existing measures. To facilitate the interactive or interdependent features among elements in a set, new Shapley-weighted divergence measures for IFSs are developed via the eminent Shapley function, which can be perceived as generalization of the allied weighted divergence measures. Furthermore, we develop Shapley-weighted divergence measures based VIKOR method, which is stimulated by conventional VIKOR method. The proposed method is more adaptable and sinuous for correlative decision-making problems, which is used to determine the ranking order of alternatives and find the optimal one(s), so that it is surmounted the difficulty of the decision makers. To demonstrate the validity of the proposed method, numerical examples related to pattern recognition and multi-criteria decision making are presented, which displays the advantages and feasibility.