Generalized C<inf>F<inf>1</inf>F<inf>2</inf></inf>-integrals: From Choquet-like aggregation to ordered directionally monotone functions

Dimuro, GP; Lucca, G; Bedregal, B; Mesiar, R; Sanz, JA; Lin, CT; Bustince, H

Generalized C<inf>F<inf>1</inf>F<inf>2</inf></inf>-integrals: From Choquet-like aggregation to ordered directionally monotone functions

Dimuro, GP Lucca, G Bedregal, B Mesiar, R Sanz, JA Lin, CT

Bustince, H

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Publication Type:: Journal Article
Citation:: Fuzzy Sets and Systems, 2020, 378 pp. 44 - 67
Issue Date:: 2020-01-01

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Field	Value	Language
dc.contributor.author	Dimuro, GP	en_US
dc.contributor.author	Lucca, G	en_US
dc.contributor.author	Bedregal, B	en_US
dc.contributor.author	Mesiar, R	en_US
dc.contributor.author	Sanz, JA	en_US
dc.contributor.author	Lin, CT https://orcid.org/0000-0001-8371-8197	en_US
dc.contributor.author	Bustince, H	en_US
dc.date.available	2021-01-21T18:06:33Z
dc.date.issued	2020-01-01	en_US
dc.identifier.citation	Fuzzy Sets and Systems, 2020, 378 pp. 44 - 67	en_US
dc.identifier.issn	0165-0114	en_US
dc.identifier.uri	http://hdl.handle.net/10453/132584
dc.description.abstract	© 2019 Elsevier B.V. This paper introduces the theoretical framework for a generalization of CF1F2-integrals, a family of Choquet-like integrals used successfully in the aggregation process of the fuzzy reasoning mechanisms of fuzzy rule based classification systems. The proposed generalization, called by gCF1F2-integrals, is based on the so-called pseudo pre-aggregation function pairs (F1,F2), which are pairs of fusion functions satisfying a minimal set of requirements in order to guarantee that the gCF1F2-integrals to be either an aggregation function or just an ordered directionally increasing function satisfying the appropriate boundary conditions. We propose a dimension reduction of the input space, in order to deal with repeated elements in the input, avoiding ambiguities in the definition of gCF1F2-integrals. We study several properties of gCF1F2-integrals, considering different constraints for the functions F1 and F2, and state under which conditions gCF1F2-integrals present or not averaging behaviors. Several examples of gCF1F2-integrals are presented, considering different pseudo pre-aggregation function pairs, defined on, e.g., t-norms, overlap functions, copulas that are neither t-norms nor overlap functions and other functions that are not even pre-aggregation functions.	en_US
dc.relation.ispartof	Fuzzy Sets and Systems	en_US
dc.relation.isbasedon	10.1016/j.fss.2019.01.009	en_US
dc.subject.classification	Artificial Intelligence & Image Processing	en_US
dc.title	Generalized C<inf>F<inf>1</inf>F<inf>2</inf></inf>-integrals: From Choquet-like aggregation to ordered directionally monotone functions	en_US
dc.type	Journal Article
utslib.citation.volume	378	en_US
utslib.for	0101 Pure Mathematics	en_US
utslib.for	0801 Artificial Intelligence and Image Processing	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Computer Science
pubs.organisational-group	/University of Technology Sydney/Strength - CAI - Centre for Artificial Intelligence
utslib.copyright.status	open_access	*
pubs.publication-status	Published	en_US
pubs.volume	378	en_US

Abstract:

© 2019 Elsevier B.V. This paper introduces the theoretical framework for a generalization of CF1F2-integrals, a family of Choquet-like integrals used successfully in the aggregation process of the fuzzy reasoning mechanisms of fuzzy rule based classification systems. The proposed generalization, called by gCF1F2-integrals, is based on the so-called pseudo pre-aggregation function pairs (F1,F2), which are pairs of fusion functions satisfying a minimal set of requirements in order to guarantee that the gCF1F2-integrals to be either an aggregation function or just an ordered directionally increasing function satisfying the appropriate boundary conditions. We propose a dimension reduction of the input space, in order to deal with repeated elements in the input, avoiding ambiguities in the definition of gCF1F2-integrals. We study several properties of gCF1F2-integrals, considering different constraints for the functions F1 and F2, and state under which conditions gCF1F2-integrals present or not averaging behaviors. Several examples of gCF1F2-integrals are presented, considering different pseudo pre-aggregation function pairs, defined on, e.g., t-norms, overlap functions, copulas that are neither t-norms nor overlap functions and other functions that are not even pre-aggregation functions.

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http://hdl.handle.net/10453/132584