Determining the fuzzy measures in multiple criteria decision aiding from the tolerance perspective

We consider multiple criteria decision aiding (MCDA) in the case of interactions between criteria. In dealing with interactions between criteria, fuzzy measures and integrals have demonstrated great advantages. Nevertheless, the determination of fuzzy measures has proven difficult because the capacities of not only single criterion but also all subsets of criteria need to be identified. Due to the value judgment essence of MCDA, the attitudes of the decision maker (DM) are typically modeled to identify fuzzy measures. In this paper, the tolerance attitudes of the DM, which implies a direct requirement instead of partial preference, are modeled with regard to the determination of fuzzy measures for the first time. With two scales developed in this paper, the DM can directly express the tolerance attitudes to certain criteria other than providing partial preference through pairwise comparison. As a result, it requires less prior knowledge and is more efficient to some extent. Further, the inherent interacting mechanism of criteria under different tolerance attitudes is explored. At last, the tolerance attitudes are applied to the process of multiple criteria analysis using a Choquet integral. A classic student evaluation problem is given as an example. The evaluation results are compared with additive models. This paper not only provides a new inspiration to the determination of fuzzy measures but also improves the descriptive capacity of fuzzy measures to the real world.