Weakly Prioritized Measure Aggregation in Prioritized Multicriteria Decision Making

This paper mainly investigates a special kind of multicriteria decision-making problem, in which all the criteria can be divided into several hierarchies and the criteria in the higher hierarchy have priorities over those in the lower hierarchy. It implies that the loss of the higher priority criterion can't be compensated by the gain of the lower prioritized criteria. As we know, fuzzy measures can well represent the interactions between criteria. In this situation, we develop a new fuzzy measure called weakly ordered prioritized measure (WOPM) to express the priority rule among the weakly ordered prioritized criteria. On the basis of the WOPM, we use discrete Choquet integral to construct a new WOPM-guided aggregation (WOPMGA) operator. To understand the priority property of this aggregation operator deeply, we get all the criteria's Shapley values and make an analysis of all criteria's Shapley values with different parameter values. Through analysis, we can find that the WOPMGA operator has the properties of boundedness, idempotency and monotonicity. Finally, we give several practical examples to illustrate the effectiveness of this aggregation operator.