Novel optimistic and pessimistic family of OWA operator with constant orness

Abstract

In this paper, we present a novel representative of the existing family of ordered weighted aggregation (OWA) operators with constant orness (optimism/pessimism level). In other words, orness value of weight vectors generated using the proposed operator is independent of the total number of arguments. The proposed OWA operator is the operator that is based on the beta function. Two different types of operators have been proposed with respect to the level of optimism (“or-like”) and pessimism (“and-like”) each. In addition to that the proposed operators discussed here are bi-parametric and real-valued in nature in terms of their parameters. Hence, for a given orness value (optimism or pessimism), it provides an infinite number of weight vectors as the proposed operator's orness depends on the value of one of its parameters. These properties lead to lots of flexibility for the Decision-Maker (DM). Its comparison and advantages over other existing members of the OWA family with constant orness such as S-OWA operators have been elaborated. Also, the maximum Rényi entropy of the OWA (MRE-OWA) operator and the maximum Rényi entropy of the proposed OWA operator are compared and evaluated for a specified orness level. Several other important properties and applications of the family of the proposed operators have also been analyzed in detail.