Three-way decision based on third-generation prospect theory with Z-numbers

摘要

Three-way decision provides a practical and updated research orientation to deal with decision problems. In this article, a new three-way decision model combined with Z numbers and third-generation prospect theory is proposed. To construct the proposed model, Z-numbers are utilized to depict the decision information containing in the outcome matrix, uncertain reference points, and information table. All the Z-numbers are transformed into triangular fuzzy numbers for better calculating and processing to achieve this goal. The triangular fuzzy value functions and cumulative decision weights of the proposed model are determined based on third-generation prospect theory to derive maximum-prospect-value decision rules. Then, the properties and thresholds of decision rules are discussed and analyzed under Z-information environment. Considering a universal circumstance that there are no decision attributes in the information system, we utilize two multi-attribute decision-making methods with Z-numbers to estimate the conditional probability. Both two methods involve third-generation prospect theory for representing the risk attitude and preference of decision-makers. An illustrative example of the task assessment problem is presented to verify the efficacy of our model. Finally, we take the comparative analysis and some experiments to show the proposed model's performance and characteristics.