Empirical Monotonicity of Non-deterministic Computable Aggregations
Luis Garmendia, Daniel Gómez, Luis Magdalena, Javier Montero · Atlantis studies in uncertainty modelling/Atlantis Studies in Uncertainty Modelling · 2021
The concept of aggregation has been usually associated with that of aggregation functions, assuming that any aggregation process can be represented by a function.Recently, computable aggregations have been introduced considering that the core of the aggregation processes is the program that enables it.In this new framework, the concept of monotonicity of an aggregation, linked to the monotonicity of the function defining the aggregation, should be revisited once there is not such a function.The new concept of aggregation also opens a new scenario where the aggregation can even be nondeterministic.Assuming these premises, the present work focuses on monotonicity of nondeterministic computable aggregations, considering the situation where the program implementing the aggregation is a black box, that is, only inputs and outputs are available.But due to non-determinism, a certain input will not always produce the same output, and the analysis should be based on multiple executions of the program, generating for that single input a collection of outputs (a list) that could be analysed as such, or interpreted as a distribution.Monotonicity analysis will require the comparison of those lists of outputs in terms of ordering, and to do so it is needed the previous definition of an order relation in the set of lists.