A comparative study of optimistic and pessimistic multicriteria decision analysis based on atanassov fuzzy sets

Abstract

Following the unipolar bivariate model, this paper presents a useful method of relating optimism and pessimism to multiple criteria decision analysis within the context of Atanassov fuzzy sets. We utilize four point operators to readily estimate the adaptational outcome expectancies generated by optimistic and pessimistic attitudes. We then determine the net predisposition to represent the aggregated effects of positive and negative evaluations. On the basis of the net predispositions, we calculate the suitability function to evaluate each alternative. Accordingly, we propose the optimization model with suitability functions to deal with ill-known grades of importance. We develop algorithms to aid multicriteria decision-making processes under neutral, completely optimistic, moderately optimistic, completely pessimistic, and moderately pessimistic conditions. Furthermore, we present experimental analysis on randomly generated decision problems to investigate the ranking system's consistency and the ranking irregularity issues found in the proposed methods. We establish several valuable test criteria to discuss some types of ranking consistency and irregularities (e.g., ranking consistency, ranking correlations, ranking contradictions, and ranking inversions) that occur when the different methods are used. We designed three computational experiments to compare the ranking orders yielded by different methods and examined several comparison indices, including the consistency rate of the total orders, the contradiction rate of the best choice, and the inversion rate between the better choices and the worse ones. Finally, we provided a second-order regression model to highlight the effects of variant parameter settings on the average Spearman rank correlation coefficients.