A new multi-criteria evaluation model based on the combination of non-additive fuzzy AHP, Choquet integral and Sugeno λ-measure

Abstract

This paper proposes a new model for multi-criteria evaluation under uncertain condition. In this model we consider the interaction between criteria as one of the most challenging issues especially in the presence of uncertainty. In this case usual pairwise comparisons and weighted sum cannot be used to calculate the importance of criteria and to aggregate them. Our model is based on the combination of non-additive fuzzy linguistic preference relation AHP (FLPRAHP), Choquet integral and Sugeno λ-measure. The proposed model capture fuzzy preferences of users and fuzzy values of criteria and uses Sugeno λ-measure to determine the importance of criteria and their interaction. Then, integrating Choquet integral and FLPRAHP, all the interaction between criteria are taken in to account with least number of comparison and the final score for each alternative is determined. So we would model a comprehensive set of interactions between criteria that can lead us to more reliable result. An illustrative example presents the effectiveness and capability of the proposed model to evaluate different alternatives in a multi-criteria decision problem.