Multi-criteria decision-making method with leniency reduction based on interval-valued fuzzy sets

The purpose of this article is to present a useful method for estimating the importance of criteria and reducing the leniency bias in multi-criteria decision analysis based on interval-valued fuzzy sets. Several types of net predispositions are defined to represent an aggregated effect of interval-valued evaluations. The suitability function to measure the overall evaluation of each alternative is then determined based on simple additive weighting (SAW) methods. Another method, the relative closeness of each alternative to the positive-ideal solution, can also be obtained by net predispositions when using the technique for order preference by similarity to ideal solution (TOPSIS). Because positive or negative leniency may exist when most criteria are assigned unduly high and low ratings, respectively, some deviation variables are introduced to mitigate the effects of overestimated and underestimated ratings on criterion importance. Considering the two objectives of maximal weighted suitability (or maximal closeness coefficient) and minimal deviation values, an integrated programming model is proposed to compute the optimal weights for the criteria and the corresponding suitability degrees (or closeness coefficient values) for alternative rankings. Flexible algorithms with SAW and TOPSIS methods are established by considering both objective and subjective information to compute optimal multi-criteria decisions. Finally, the feasibility and effectiveness of the proposed methods are illustrated by a numerical example.