RT Journal Article
T1 Analysing monotonicity in non-deterministic computable aggregations: The probabilistic case
A1 Luis Magdalena, 
A1 Gómez González, Daniel
A1 Garmendia Salvador, Luis
A1 Montero De Juan, Francisco Javier
AB The idea of computable aggregation operators was introduced as a generalization of aggregation operators, allowing the replacement of the mathematical function usually considered for aggregation, by a program that performs the aggregation process. There are different reasons to justify this extension. One of them is the interest in exploring some computational properties not directly related to the aggregation itself but to its implementation (complexity, recursivity, parallelisation, etc). Another reason, the one driving to the present paper, is the need to define a framework where the quite common process of first sampling (over a large data set) and then aggregating the sample, could be analysed as a formal aggregation process. This process does not match with the idea of an aggregation function, due to its non-deterministic nature, but could easily be adapted to that of a (non-deterministic) computable aggregation. The idea of non-deterministic aggregation requires the extension of the concept of monotonicity (a key aspect of aggregation operators) to this new framework. The present paper will explore this kind of non-deterministic aggregation processes, first from an empirical point of view and then in terms of populations, adapting the idea of monotonicity to both of them and finally defining a common framework for its analysis.
PB ELSEVIER
SN 0020-0255
YR 2022
FD 2022-01
LK https://hdl.handle.net/20.500.14352/113496
UL https://hdl.handle.net/20.500.14352/113496
LA eng
NO Luis Magdalena, Daniel Gómez, Luis Garmendia, Javier Montero, Analysing monotonicity in non-deterministic computable aggregations: The probabilistic case, Information Sciences, Volume 583, 2022, Pages 288-305, ISSN 0020-0255, https://doi.org/10.1016/j.ins.2021.11.015. (https://www.sciencedirect.com/science/article/pii/S0020025521011257) Abstract: The idea of computable aggregation operators was introduced as a generalization of aggregation operators, allowing the replacement of the mathematical function usually considered for aggregation, by a program that performs the aggregation process. There are different reasons to justify this extension. One of them is the interest in exploring some computational properties not directly related to the aggregation itself but to its implementation (complexity, recursivity, parallelisation, etc). Another reason, the one driving to the present paper, is the need to define a framework where the quite common process of first sampling (over a large data set) and then aggregating the sample, could be analysed as a formal aggregation process. This process does not match with the idea of an aggregation function, due to its non-deterministic nature, but could easily be adapted to that of a (non-deterministic) computable aggregation. The idea of non-deterministic aggregation requires the extension of the concept of monotonicity (a key aspect of aggregation operators) to this new framework. The present paper will explore this kind of non-deterministic aggregation processes, first from an empirical point of view and then in terms of populations, adapting the idea of monotonicity to both of them and finally defining a common framework for its analysis. Keywords: Aggregation; Computable aggregation; Non-deterministic aggregation; Orders of lists; Monotonicity
DS Docta Complutense
RD 18 abr 2025