Parameterized and-Uke and or-Like Owa Operators

We discuss the OWA (Ordered Weighted Averaging) operators which provide for aggregation operations lying between the and and the or, and the BADD (BAsic Defuzzification Distribution) transformation. This transformation plays a central role in the development of defuzzification procedures, the aggregation of elements in a fuzzy subset to obtain one representative element. We suggest the use of the BADD transformation to generate a class of OWA like aggregation operators, denoted BADD-OWA operators. We show that while these BADD-OWA operators have some interesting properties, they fail to be mono-tonic. We next use another family of defuzzification operators, called SLIDE, to generate another class of OWA operators. These S-OWA operators provide two subfamilies of OWA operators, one Or-like and the other And-Like.