Constructing an Outranking Relation with Weighted OWA for Multi-criteria Decision Analysis

Abstract

Some decision aiding methods are based on constructing and exploiting outranking relations. An alternative a outranks another b if a is at least as good as b (aSb). One well known method in this field is ELECTRE. The outranking relation is usually built by means of a weighted average (WA) of the votes given by a set of criterion with respect to the fulfilment of aSb. The value obtained represent the strength of the majority opinion. The WA operator can be observed to have sometimes an undesired compensative effect. In this paper we propose the use of other aggregation operators with different mathematical properties. In particular, we substitute the WA by three operators from the Ordered Weighted Average (OWA) family of operators because it permits to decide the degree of andness/orness that is used during the aggregation. The OWAWA (Ordered Weighted Average Weighted Average), WOWA (Weighted Ordered Weighted Average) and IOWA (Induced Ordered Weighted Average) operators are studied. They are capable to combine the importance given to each criterion with the conjunctive/disjunctive requirement applied in the definition of the outranking relation.