Extended and infinite ordered weighted averaging and sum operators with numerical examples

Abstract

This study discusses some variants of Ordered Weighted<br />Averaging (OWA) operators and related information aggregation methods. In<br />detail, we define the Extended Ordered Weighted Sum (EOWS) operator and the<br />Extended Ordered Weighted Averaging (EOWA) operator, which are applied in<br />scientometrics evaluation where the preference is over finitely many<br />representative works. As contrast, we also define the Infinite Ordered<br />Weighted Sum (InOWS) operator and the Infinite Ordered Weighted Averaging<br />(InOWA) operator, which are more suitable for the corresponding<br />scientometrics evaluation where all of works of scholars are considered. We<br />also define the family of Infinite Gaussian maxitive OWA weights function<br />and the family of Infinite Gaussian OWA weights function, and discuss some<br />of their mathematical properties. Some illustrative examples, comparisons<br />and figures are provided to better expound their applicability in<br />scientometrics evaluation.