Population Monotonicity of Non-deterministic Computable Aggregations

Abstract

Computable aggregation operators can be seen as a generalization of aggregation operators where the mathematical function is replaced by a program that performs the aggregation process. This extension allows the introduction of new aggregation processes not feasible under the classical framework. Particularly interesting are some non-deterministic processes widely considered to merge information. However, especially in non-deterministic processes, the extension of some of the well-known concepts for aggregation operators such as monotony, is needed. In this work, a new concept of monotonicity is proposed, from a probabilistic perspective, for non-deterministic computable aggregation operators. To be consistent, the concept coincides with the classical definition in the deterministic case. In addition, some cases of interest are analysed.