Normal Fuzzy Three-Way Decision Based on Prospect Theory

Yanhua Li, Jiafen Liu, Yihua Zhong, Xin Yang

Abstract: Prospect theory-based three-way decision has been successfully applied in various fuzzy information systems owing to its excellent performance in expressing the risk attitude of decision makers. However, the current prospect theory-based three-way decisions have two following limitations. On the one hand, they are constrained in processing uncertain continuous data or neglecting the distribution of uncertain fuzzy numbers. On the other hand, the risk attitudes of decision-makers are not considered when calculating the conditional probability. To address the two issues, we propose a normal fuzzy prospect theory-based three-way decision model and a normal fuzzy ideal solution method. First, since normal fuzzy numbers can describe the continuous uncertain data subjected to the normal distribution, we use it to represent the uncertain decision information, i.e., normal fuzzy outcome matrix, normal fuzzy reference points. Then, by integrating prospect theory and TOPSIS, we propose a normal fuzzy ideal solution method to calculate conditional probability, which considers the risk attitudes of decision-makers. Finally, the comparative experiments demonstrate the effectiveness and superiority of our proposal.