Joint Proceedings of the 19th World Congress of the International Fuzzy Systems Association (IFSA), the 12th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), and the 11th International Summer School on Aggregation Operators (AGOP)

Empirical Monotonicity of Non-deterministic Computable Aggregations

Authors
Luis Garmendia, Daniel Gómez, Luis Magdalena, Javier Montero
Corresponding Author
Luis Garmendia
Available Online 30 August 2021.
DOI
https://doi.org/10.2991/asum.k.210827.073How to use a DOI?
Keywords
Aggregation, Computable aggregation, non-deterministic aggregation, partial orders of lists, monotonicity
Abstract

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 non-deterministic. Assuming these premises, the present work focuses on monotonicity of non-deterministic 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.

Copyright
© 2021, the Authors. Published by Atlantis Press.
Open Access
This is an open access article distributed under the CC BY-NC license (http://creativecommons.org/licenses/by-nc/4.0/).

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Cite this article

TY  - CONF
AU  - Luis Garmendia
AU  - Daniel Gómez
AU  - Luis Magdalena
AU  - Javier Montero
PY  - 2021
DA  - 2021/08/30
TI  - Empirical Monotonicity of Non-deterministic Computable Aggregations
BT  - Joint Proceedings of the 19th World Congress of the International Fuzzy Systems Association (IFSA), the 12th Conference of the European Society for Fuzzy Logic and Technology (EUSFLAT), and the 11th International Summer School on Aggregation Operators (AGOP)
PB  - Atlantis Press
SP  - 554
EP  - 561
SN  - 2589-6644
UR  - https://doi.org/10.2991/asum.k.210827.073
DO  - https://doi.org/10.2991/asum.k.210827.073
ID  - Garmendia2021
ER  -