Probabilistic Linguistic Matrix Game Based on Fuzzy Envelope and Prospect Theory with Its Application

Abstract

Game theory is a powerful tool in modeling strategic interaction among rational players. However, as practical problems become more complex, uncertainty inevitably appears in the game. Due to the advantages of probabilistic linguistic term sets (PLTSs) in comprehensively and flexibly portraying uncertainty, fuzziness and hesitancy, this paper uses PLTSs to express players’ payoff values, and aims to develop an integrated method based on fuzzy envelope and prospect theory (PT) under a probabilistic linguistic environment for solving matrix games. In this method, an improved probabilistic ordered weighted averaging (POWA) operator is defined. Then, a novel trapezoidal fuzzy envelope for PLTSs is proposed and some related theorems are analyzed. Next, based on the defined cosine distance measure for PLTSs, the players’ psychological behavior in the game is considered by establishing the prospect value function. Besides, the applicability and practicability of the proposed method is verified with an example from the development strategy of Sanjiangyuan National Nature Reserve (SNNR) in China. Finally, some comparative analyses are carried out to illustrate the superiority of the proposed method. In order to improve the application of this proposed method, a decision support system (DSS) based on it is designed.