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A constructive framework to define fusion functions with floating domains in arbitrary closed real intervals
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SYSNO ASEP 0564676 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title A constructive framework to define fusion functions with floating domains in arbitrary closed real intervals Author(s) Asmus, T. C. (BR)
Dimuro, G. P. (BR)
Bedregal, B. (BR)
Sanz, J. A. (ES)
Fernandez, J. (ES)
Rodriguez-Martinez, I. (ES)
Mesiar, Radko (UTIA-B) RID, ORCID
Bustince, H. (ES)Number of authors 8 Source Title Information Sciences. - : Elsevier - ISSN 0020-0255
Roč. 610, č. 1 (2022), s. 800-829Number of pages 30 s. Publication form Print - P Language eng - English Country US - United States Keywords (a,b)-Aggregation functions ; (a,b)-Fusion functions ; n-Dimensional overlap functions ; t-conorms ; t-norms ; uninorms Subject RIV BA - General Mathematics OECD category Applied mathematics Method of publishing Limited access Institutional support UTIA-B - RVO:67985556 UT WOS 000860782400010 EID SCOPUS 85135958796 DOI 10.1016/j.ins.2022.08.007 Annotation Fusion functions and their most important subclass, aggregation functions, have been successfully applied in fuzzy modeling. However, there are practical problems, such as classification via Convolutional Neural Networks (CNNs), where the data to be aggregated are not modeling membership degrees in the unit interval. In this scenario, systems could benefit from the application of operators defined in domains different from [0,1], although, presenting similar behavior of some aggregation functions whose subclasses are currently defined only in the fuzzy context (e.g., overlap functions and t-norms). So, the main objective of this paper is to present a general framework to characterize classes of fusion functions with floating domains, called (a,b)-fusion functions, defined on any closed real interval [a,b], based on classes of core fusion functions defined on [0,1]. The fundamental aspect of this framework is that the properties of a core fusion function are preserved in the context of the analogous (a,b)-fusion function. Construction methods are presented, and some properties are studied. We also introduce a framework to define fusion functions in which the inputs come from an interval [a,b] but the output is mapped on a possibly different interval [c,d]. Finally, we present an illustrative example in image classification via CNNs. Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2023 Electronic address https://www.sciencedirect.com/science/article/pii/S0020025522008878?via%3Dihub
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