Bi-fuzzy graph cooperative game model and application to profit allocation of ecological exploitation

Abstract

Ecological exploitation research generally holds that cooperation alliances form without restrictions and the information within alliances is known exactly. However, these assumptions do not always accord with reality. The main aim of this paper is to develop a more realistic approach in order to analyze alliance formation and profit allocation from ecological exploitation. We define an extended fuzzy graph cooperative game, in which players partially participating in coalitions and payoffs are fuzzy numbers, called bi-fuzzy graph cooperative game. The average tree solution (short for A-T solution) based on players’ risk preferences is proposed for this cooperative game, and the existence of the solution is proved. This paper can demonstrate that the players’ profitability depends not only on their marginal contribution degree to the coalition, but also on the communication structure and players’ positions in coalitions of a cooperative game.