Solving hesitant fuzzy linguistic matrix game problems for multiple attribute decision making with prospect theory

Game theory is powerful to solve the multiple attribute decision making problems, in this paper, we propose a matrix game method from the perspective of the decision maker and Nature. The purpose of the decision maker is not gaining the maximum benefit in the short term, but to realize the sustainable development of mankind and Nature in the long run. The payoffs of matrix game are represented by the hesitant fuzzy linguistic information which portrays the uncertainty and fuzziness in an effective and flexible way. A modified method is proposed to aggregate the hesitant fuzzy linguistic information. Because decision makers show the risk-seeking tendency for gains and the risk-averse tendency for losses, the prospect theory under the hesitant fuzzy linguistic circumstance is investigated. Then the hesitant fuzzy nonlinear programming models for the decision maker and Nature are established and the optimal solution is obtained. Furthermore, the proposed method is applied to determine importance ranking of the alternatives when developing the economic strategies in Sanjiangyuan National Nature Reserve, China. Finally, the comparative analysis is designed to verify the availability and reasonability of the proposed method.