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A penalty-based aggregation operator for non-convex intervals

Beliakov, G and James, S 2014, A penalty-based aggregation operator for non-convex intervals, Knowledge-based systems, vol. 70, pp. 335-344, doi: 10.1016/j.knosys.2014.07.011.

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Title A penalty-based aggregation operator for non-convex intervals
Author(s) Beliakov, GORCID iD for Beliakov, G orcid.org/0000-0002-9841-5292
James, SORCID iD for James, S orcid.org/0000-0003-1150-0628
Journal name Knowledge-based systems
Volume number 70
Start page 335
End page 344
Publisher Elsevier BV
Place of publication Amsterdam, The Netherlands
Publication date 2014-11-01
ISSN 0950-7051
Keyword(s) aggregation functions
averaging operators
hesitant fuzzy sets
interval-valued fuzzy sets
penalty-based functions
Summary In the case of real-valued inputs, averaging aggregation functions have been studied extensively with results arising in fields including probability and statistics, fuzzy decision-making, and various sciences. Although much of the behavior of aggregation functions when combining standard fuzzy membership values is well established, extensions to interval-valued fuzzy sets, hesitant fuzzy sets, and other new domains pose a number of difficulties. The aggregation of non-convex or discontinuous intervals is usually approached in line with the extension principle, i.e. by aggregating all real-valued input vectors lying within the interval boundaries and taking the union as the final output. Although this is consistent with the aggregation of convex interval inputs, in the non-convex case such operators are not idempotent and may result in outputs which do not faithfully summarize or represent the set of inputs. After giving an overview of the treatment of non-convex intervals and their associated interpretations, we propose a novel extension of the arithmetic mean based on penalty functions that provides a representative output and satisfies idempotency.
Language eng
DOI 10.1016/j.knosys.2014.07.011
Field of Research 080108 Neural, Evolutionary and Fuzzy Computation
Socio Economic Objective 970108 Expanding Knowledge in the Information and Computing Sciences
HERDC Research category C1 Refereed article in a scholarly journal
ERA Research output type C Journal article
Copyright notice ©2014, Elsevier
Free to Read? Yes
Persistent URL http://hdl.handle.net/10536/DRO/DU:30067739

Document type: Journal Article
Collections: School of Information Technology
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Scopus Citation Count Cited 6 times in Scopus
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Created: Tue, 25 Nov 2014, 15:10:29 EST

Every reasonable effort has been made to ensure that permission has been obtained for items included in DRO. If you believe that your rights have been infringed by this repository, please contact drosupport@deakin.edu.au.