Hybrid game cross efficiency evaluation models based on interval data: A case of forest carbon sequestration

Abstract

Cross-efficiency evaluation is an effective method for the ranking of decision-making units (DMUs) in data envelopment analysis, which is the performed method for peer-evaluation and self-evaluation. In most cross-efficiency evaluation methods, the peer evaluation result is completely constrained by the evaluator's optimal self-evaluation weights. DMUs are connected by a competitive relationship; therefore, they can be regarded as players in the game and the cross efficiency value can be regarded as payment because of this competition. DMUs need to consider the impact of their own weights on other DMUs to identify a set of weights for evaluating themselves. Based on the idea of non-cooperative games in the cross evaluation of DMUs, this paper considers the interval cross game efficiency of DMUs with the interval data. The interval data theory is combined, the best production state and the worst production state are taken as reference states, and four evaluation strategy models are proposed according to the opposition and coordination relationship. Then, the bijective and injective interval game cross models, as well as the algorithm corresponding to the four evaluation strategies are constructed. Moreover, the result of the self-evaluation is used as the initial parameter to prove the existence of the solution and the convergence of the algorithm. Based on the priority relationship of the evaluation results under different strategies, the interval entropy method is used to aggregate the results and obtain the final cross efficiency of the interval game. Furthermore, both the applicability and superiority of this model are exemplified by an example. Finally, based on the method of this paper, the efficiency of forest carbon sequestration in China are studied, seven natural regions in China are ranked by forest carbon sequestration efficiency values reasonably, and the current regions development of forest carbon sequestration in China are evaluated.