A multimeasure approach to optimism and pessimism in multiple criteria decision analysis based on Atanassov fuzzy sets

The frequently used methods of handling optimism and pessimism in multiple criteria decision analysis are Hurwicz’s and Yager’s approaches. Despite their wide usage, a critical issue has been raised about unidimensionality. Numerous psychological researches and empirical findings have convincingly supported that optimism and pessimism do not represent opposite poles on a single, bipolar dimension, but they are conceived as two partially independent dimensions instead. The focus of this paper is a two-dimensional approach by adequately employing the degrees of membership and non-membership based on Atanassov fuzzy sets. This study develops optimistic and pessimistic estimations with several fuzzy point operators to draw the influences of optimism and pessimism on multicriteria decision making for the sake of a better fit than the unidimensional model. Given a typology from empirical grounds, the appropriate point operators specific to each type are suggested to identify adaptational outcomes. Base upon a series of new score functions, a useful method for multiple criteria decision analysis is provided to efficiently facilitate decision analysis with a multimeasure approach. Feasibility and effectiveness of the proposed methods are illustrated by a practical example.