Extended And Infinite Ordered Weighted Averaging And Sum Operators With Numerical Examples

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