The 2-additive fuzzy Choquet integral-based TODIM method with improved score function under hesitant fuzzy environment

Recently, the TODIM$^1$(an acronym in Portuguese of interactive and multi-criteria decision making) method has attracted increasing attention and many researchers have extended it to deal with multiple attribute decision making (MADM) problems under different situations. However, none of them can be used to handle MADM problems with positive, independent, and negative interactions among attributes, which restricts the applicability of TODIM method. Therefore, in this paper, we propose the 2-additive fuzzy Choquet integral-based hesitant fuzzy TODIM method to deal with this situation. To begin with, we propose the novel measured function to compare the magnitude of hesitant fuzzy elements, which has been proved to be more rational and efficient than existing approaches. Then we use nonlinear programming to obtain 2-additive fuzzy measures and then put forward novel Choquet integral based-dominance degree to calculate the dominance degree of one alternative over another under all attributes. Consequently, we then calculate the global value of each alternative whereby we can rank all the alternatives. Finally, an illustrate example is used to demonstrate the efficiency and applicability of the proposed approach with sensitivity analysis.