Cross-efficiency evaluation of the data envelopment analysis with conflict behaviour and beneficial relationship perspectives

In data envelopment analysis, cross-efficiency evaluation stands out as a valuable tool for ranking the effectiveness of decision-making units (DMUs). However, existing research commonly assume that DMUs are randomly classified as either collaborators or opponents of the evaluated DMUs. Unfortunately, few studies have considered the presence of conflict behaviour and beneficial relationships among DMUs during cross-efficiency evaluation. To address this research gap, this study proposes an innovative approach. Firstly, the proposed framework incorporates an interval cross-efficiency environment to accommodate the inherent uncertainty and fuzziness in the efficiency scores of DMUs. Secondly, two definitions, namely task conflict cross-efficiency and relationship conflict cross-efficiency, are introduced by combining the characteristics of the interval cross-efficiency matrix with conflict behaviour. To measure the strength of the conflict between DMUs, a novel measurement method is proposed, forming the foundation for constructing two cross-efficiency secondary programming models based on conflict behaviour. Thirdly, the Spearman's rank correlation coefficient is employed to measure the strength of beneficial relationships among DMUs. Subsequently, two cross-efficiency secondary programming models are developed based on beneficial relationships. To obtain the final scores, the efficiency scores of the four models are integrated using the Shannon entropy method. Finally, two illustrative applications are presented to demonstrate the effectiveness and robustness of the proposed method.