RIOWA: Restricted induced ordered weighted averaging operators, applied to missing data imputation

Ordered Weighted Averaging (OWA) operators and their extensions, such as Induced OWA (IOWA) operators, are widely used in the field of data fusion, as they enable the assignment of importance to each piece of data. This property is achieved by combining a set of weights with the sorting of the operator’s inputs, which is particularly valuable in applications such as missing data imputation. However, when duplicated data are present, classical ordered weighted operators cannot distinguish whether duplicates are real or a consequence of data quality problems. This may lead to undesired weights that have a bias towards repeated values rather than actual data distributions. To remove this potential bias and better adapt to dataset distributions, we introduce in this paper a new family of operators, called Restricted IOWA (RIOWA), that only operates with unique inputs. We study the fundamental properties of these operators, and we apply them to tackle the problem of missing data imputation and compare their performance against that of the original OWA and IOWA operators.