Prioritized Measure-Guided Aggregation Operators

This paper mainly investigates a particular type of multicriteria aggregation imperative called prioritized aggregations in order to handle a class of multicriteria decision making problems, in which there are prioritizations among criteria. In such problems, the satisfaction degrees of higher prioritized criteria cannot be compensated by the lower prioritized criteria. To describe the prioritizations among criteria quantitatively, Yager has introduced a prioritized measure from the viewpoint of fuzzy measure, which is validated as an effective method, except for some little imperfectness. On the basis of detailed analysis with respect to Yager's prioritized measure, we elaborate the properties of prioritized measures and then propose a generalized form of prioritized measure. Moreover, by using the generalized prioritized measure to convey the prioritized imperative, we develop a generalized prioritized measure-guided aggregation operator that is based on the Choquet integral. Additionally, the prioritized weight aggregation operator, introduced by Yager, is verified to be a special case of the generalized prioritized measure-guided aggregation operator. At length, we develop a concrete prioritized measure and the corresponding prioritized measure-guided aggregation operator under the framework of the generalized prioritized measure-guided aggregation operator and illustrate their feasibility and effectiveness through several numerical examples.