Web-Geometric View on Uninorms and Structure of Some Special Classes

0379838 - ÚI 2013 RIV DE eng C - Conference Paper (international conference)
Petrík, Milan - Mesiar, R.
Web-Geometric View on Uninorms and Structure of Some Special Classes.
Advances in Computational Intelligence. Heidelberg: Springer, 2012 - (Greco, S.; Bouchon-Meunier, B.; Coletti, G.; Fedrizzi, M.; Matarazzo, B.; Yager, R.), s. 370-378. Communications in Computer and Information Science, 299. ISBN 978-3-642-31717-0. ISSN 1865-0929.
[IPMU 2012 /14./. Catania (IT), 09.07.2012-13.07.2012]
R&D Projects: GA ČR GPP201/12/P055
Grant - others:GA MŠk(CZ) EE2.3.20.0051
Institutional support: RVO:67985807
Keywords : associativity * contour * level set * Reidemeister closure condition * structural characterization * underlying triangular norm * underlying triangular conorm * uninorm * web geometry
Subject RIV: BA - General Mathematics

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).
Permanent Link: http://hdl.handle.net/11104/0210705