An extended TODIM method for hesitant fuzzy interactive multicriteria decision making based on generalized Choquet integral

As a kind of behavior decision-making theory, TODIM (an acronym in Portuguese of interactive and multicriteria decision making (MCDM)) method has received more attention, in which the criteria values are in the format of crisp numbers. It can't be used to handle uncertain MCDM problems. In this paper, an extended Choquet-based TODIM method is proposed to solve the hesitant fuzzy MCDM problems, where interactive phenomena among criteria are also considered. First, according to fuzzy measure, the interactive criteria weight is measured by Shapley value. Then the prospect value of criteria for every alternative is calculated through prospect value function of the hesitant fuzzy set. Further, the dominance degree of each alternative over the others is calculated by Choquet integral, the global value of each alternative can be obtained to rank the alternatives. Finally, an illustrate example is given to illustrates the application of the novel method where the influence on decision making for different parameters of value function and different decision-making reference point is discussed.