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Web-Geometric View on Uninorms and Structure of Some Special Classes
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SYSNO ASEP 0379838 Document Type C - Proceedings Paper (int. conf.) R&D Document Type Conference Paper Title Web-Geometric View on Uninorms and Structure of Some Special Classes Author(s) Petrík, Milan (UIVT-O) RID, SAI, ORCID
Mesiar, R. (CZ)Source Title Advances in Computational Intelligence. - Heidelberg : Springer, 2012 / Greco S. ; Bouchon-Meunier B. ; Coletti G. ; Fedrizzi M. ; Matarazzo B. ; Yager R. R. - ISSN 1865-0929 - ISBN 978-3-642-31717-0 Pages s. 370-378 Number of pages 9 s. Publication form Print - P Action IPMU 2012 /14./ Event date 09.07.2012-13.07.2012 VEvent location Catania Country IT - Italy Event type WRD Language eng - English Country DE - Germany Keywords associativity ; contour ; level set ; Reidemeister closure condition ; structural characterization ; underlying triangular norm ; underlying triangular conorm ; uninorm ; web geometry Subject RIV BA - General Mathematics R&D Projects GPP201/12/P055 GA ČR - Czech Science Foundation (CSF) Institutional support UIVT-O - RVO:67985807 EID SCOPUS 84868157446 DOI https://doi.org/10.1007/978-3-642-31718-7_39 Annotation This paper studies the relation between associativity of uninorms and geometry of their level sets which is enabled by adopting the concepts of web geometry, a branch of differential geometry, and the Reidemeister closure condition. Based on this result, the structure of some special classes of uninorms is described. Namely, it is the class of uninorms with involutive underlying t-norms and t-conorms and the class of uninorms with involutive underlying t-norms and idempotent underlying t-conorm (as well as the corresponding dual cases). Workplace Institute of Computer Science Contact Tereza Šírová, sirova@cs.cas.cz, Tel.: 266 053 800 Year of Publishing 2013
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