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The axiomatization of asymmetric disjunction and conjunction
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SYSNO ASEP 0531644 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title The axiomatization of asymmetric disjunction and conjunction Author(s) Hudec, M. (SK)
Mesiar, Radko (UTIA-B) RID, ORCIDNumber of authors 2 Source Title Information Fusion. - : Elsevier - ISSN 1566-2535
Roč. 53, č. 1 (2020), s. 165-173Number of pages 9 s. Publication form Print - P Language eng - English Country NL - Netherlands Keywords And if possible operators ; Averaging functions ; Or else operators Subject RIV BA - General Mathematics OECD category Applied mathematics Method of publishing Open access Institutional support UTIA-B - RVO:67985556 UT WOS 000488995000016 EID SCOPUS 85067814416 DOI 10.1016/j.inffus.2019.06.018 Annotation In many real-world cases, disjunction is expressed as the fusion of full alternatives and less relevant ones, which leads to an OR ELSE connective. Obviously, this connective, so-called intensified disjunction, should provide a solution lower than or equal to the MAX operator, and higher than or equal to the projection of the full alternative. Further, to cover the cases when higher satisfaction degrees to the less relevant alternative cause that it becomes the full alternative, non–continuous asymmetric disjunction is required. The dual observation holds for the fusion of constraints (hard conditions) and wishes (soft conditions) expressed by an AND IF POSSIBLE connective. In order to cover these requirements, the paper focuses on developing a full axiomatization of asymmetric disjunction and asymmetric conjunction by averaging functions. Next, the necessity and sufficiency for associative behaviour have been proven. Moreover, the non-dual cases are also documented. Finally, the obtained results are illustrated on examples, and their applicability is also discussed. Workplace Institute of Information Theory and Automation Contact Markéta Votavová, votavova@utia.cas.cz, Tel.: 266 052 201. Year of Publishing 2021 Electronic address https://www.sciencedirect.com/science/article/pii/S1566253518308510
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