Nonadditive best-worst method

Incorporating criteria interaction using the Choquet integral

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Abstract

The best-worst method (BWM) is a multicriteria decision-making (MCDM) method to derive the relative importance (weight) of a set of criteria used to evaluate a set of alternatives. Several models (e.g., nonlinear, linear, Bayesian, and multiplicative) have been developed to find the weights based on the provided pairwise comparisons, conducted among the criteria, by the decision-maker(s)/expert(s). The existing BWM models, however, do not handle interactions that might exist between the criteria encountered in a decision problem. In this study, a nonadditive BWM is developed that considers possible interactions between the criteria. To this end, we use the Choquet integral, one of the most widely accepted techniques, to incorporate criteria interactions. A nonlinear optimization model is introduced to minimize the maximum deviation of the obtained weights from the provided pairwise comparisons, considering the information about the interactions between the criteria. We then introduce a linear variant of the nonadditive BWM and discuss its property compared to the nonlinear model. The applicability of the proposed approach is demonstrated through a real-world case study of a battery-powered electric vehicle (BEV) selection problem.