A consensual group ELECTRE-SORT approach considering the incomparable classes with the application of machine maintenance strategy assignment

Group sorting problems have attracted extensive attention, which have been successfully applied to support management decisions. However, these existing studies rarely involve the incomparable classes and the group participant may lead to the sorting conflict. Thus, in face of the group sorting problem based on the incomparable classes, by learning ELECTRE-SORT and experts’ evaluations, this paper proposes a consensual group ELECTRE-SORT approach to obtain a hierarchical structure of the incomparable classes and further determine the consensual sorting result. Specifically, for describing the consensus of the hierarchical structure, we transform the credibility matrix of central profile into 0–1 matrix to establish the consensus index of the hierarchical structure of the incomparable classes. Based on the consensual hierarchical structure, we design the consensus index of mixed classes in incomparable situation. Considering the different adjustment motivations of experts on each criterion, we introduce cost sensitivity and adjustment tolerance. In this case, we further develop a minimum cost sensitivity adjustment model in view of the credibility matrix of central profile and sorting results. Finally, we use an example of assigning machines to incomparable maintenance strategies to explain our proposed consensual GELECTRE-SORT in detail. We also perform a comparative analysis to verify the effectiveness of our proposed method.