Interval-valued fuzzy TOPSIS method with leniency reduction and an experimental analysis

The purpose of this paper is to present a new TOPSIS (the technique for order preference by similarity to ideal solution) for estimating the importance of criteria and reducing the leniency bias in multiple-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 relative closeness of each alternative to the ideal solution is then determined by net predispositions. Because positive or negative leniency may exist when most criteria are assigned unduly high or 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 closeness coefficient and minimal deviation values, an integrated programming model is proposed to compute optimal weights for the criteria and corresponding closeness coefficients for alternative rankings. A flexible algorithm using interval-valued fuzzy TOPSIS methods is established by considering both objective and subjective information to compute optimal multiple-criteria decisions. The feasibility and effectiveness of the proposed methods are illustrated by a numerical example. Finally, an experimental analysis of interval-valued fuzzy rankings given different conditions for the criterion weights is conducted with discussions on average Spearman correlation coefficients and contradiction rates.