Multi-criteria decision-making methods with optimism and pessimism based on Atanassov's intuitionistic fuzzy sets

Abstract

The theory of Atanassov's intuitionistic fuzzy sets (A-IFSs) developed over the last several decades has found useful application in fields requiring multiple-criteria decision analysis. Since the membership–nonmembership pair in A-IFSs belongs to the bivariate unipolarity type, this article describes an approach that relates optimism and pessimism to multi-criteria decision analysis in an intuitionistic fuzzy-decision environment. First, several optimistic and pessimistic point operators were defined to alter the estimation of decision outcomes. Next, based on the core of the estimations, optimistic and pessimistic score functions were developed to evaluate each alternative with respect to each criterion. The suitability function was then established to determine the degree to which each an alternative satisfies the decision maker's requirement. Because the information on multiple criteria corresponding to decision importance is often incomplete, this study included suitability functions in the optimisation models to account for poorly known membership grades. Using a linear equal-weighted summation method, these models were transformed into a single objective optimisation model to generate the optimal weights for criteria. The feasibility and effectiveness of the proposed methods were illustrated through a practical example. Finally, computational experiments with enormous amounts of simulation data were designed to conduct a comparative analysis on the ranking orders yielded by different optimistic/pessimistic point operators.

Keywords:

• Atanassov's intuitionistic fuzzy set
• multiple-criteria decision analysis
• optimism
• pessimism
• point operator
• score function
• optimisation model
• computational experiment