The Type-1 OWA Operator and the Centroid of Type-2 Fuzzy Sets

Abstract

This paper aims to establish the relationship between two apparent disparate problems: (i) the aggregation of uncertain information modelled by type-1 fuzzy sets via OWA mechanism, and (ii) the computation of the centroid of type-2 fuzzy sets. In order to cut down the computational complexity of the direct approach to performing type-1 OWA operation, the α-level approach to type-1 OWA operators was developed. This new approach is based on the decomposition of a type-1 OWA operator via its α-levels and the corresponding Representation Theorem of type-1 OWA operators. A close inspection of the mathematical representation of the centroid of type-2 fuzzy sets reveals that this is a special case of type-1 OWA operator. This relationship will allow for the computation of the centroid of a general type-2 fuzzy sets to be carried out via the application of the representation theorem to its equivalent type-1 OWA representation.