On Properties of Type-1 OWA Operators in Aggregating Uncertain Information for Soft Decision Making

The type-1 OWA operator is a new aggregation operator that is used to directly aggregate fuzzy sets via an OWA mechanism. In this paper, an α-level type-1 OWA operator capable of aggregating the α-cuts of fuzzy sets is proposed. Based on the fuzzy set Representation Theorem, we indicate that a general type-1 OWA operator can be represented by its α-level type-1 OWA operators. This result is very useful in investigating the properties of general type-1 OWA operators. In this paper, we give the conditions under which the type-1 OWA operator possesses the properties that Yager’s OWA operator holds: idempotency, monotony, compensativity, and commutativity. This provides a solid basis for the type-1 OWA operator to be applied to multi-expert decision making, multi-criteria decision making and multi-expert multicriteria decision making.