Generalized Prioritized Multicriteria Aggregation

After investigating prioritized multicriteria decision‐making or aggregation problems in depth, we reveal that priority relationships among criteria may be incomplete. In a complex and practical multicriteria decision‐making problem, the relationships of a pair of criteria can be multiform including priority relationships, except for independence. For such cases, we present a generalized prioritized multicriteria aggregation (GPMA) model with incomplete priority relationships in this paper. First, we elaborate GPMA problems, and describe them by using a dendriform structure after designing a top‐to‐bottom method to form priority hierarchies according to the given priority relationships. Furthermore, a common process for handling GPMA problems is proposed based on the premeditation that the weights associated with the lower‐priority criteria need to be revised according to the satisfaction of the higher‐priority criteria. At length, we develop two GPMA operators with respect to the GPMA with strictly and weakly ordered prioritizations, respectively, based on triangular norms, and we verify that both of them are aggregation functions.