On the properties of equidifferent OWA operator

Abstract

Getting OWA weights under given orness level is an active topic in the OWA operator research. The paper proposes a series of weights generating methods in equidifferent forms. Similar to the geometric (maximum entropy) OWA operator, we propose a parameterized OWA operator called equidifferent OWA operator, which consist the adjacent weighes with a common difference. The maximum spread equidifferent OWA (MSEOWA) operator is equivalent to the minimum variance OWA operator, but is more computational efficient. Some properties associated with the orness level are discussed. One of them is that the aggregation value for any elements set is always increasing with the orness level, which can used as a parameterized aggregation method with orness as its control parameter. These properties similar to that of the geometric (maximum entropy) OWA operator, which can also be seen as the discrete case of equidifferent RIM (regular increasing monotone) quantifiers. The general forms of equidifferent OWA operator are proposed, and the weights generating methods are also extended in a similar way.