Reconstruction of additive generators from partial derivatives of continuous Archimedean t-norms

0358541 - ÚI 2012 RIV US eng C - Conference Paper (international conference)
Navara, M. - Petrík, Milan - Sarkoci, P.
Reconstruction of additive generators from partial derivatives of continuous Archimedean t-norms.
Proceedings of the 40th IEEE International Symposium on Multple-valued logic. Los Alamitos: IEEE Computer Society, 2010, s. 241-244. ISBN 978-0-7695-4024-5. ISSN 0195-623X.
[ISMVL 2010. IEEE International Symposium on Multiple-Valued Logic /40./. Barcelona (ES), 26.05.2010-28.05.2010]
R&D Projects: GA ČR GAP202/10/1826
Institutional research plan: CEZ:AV0Z10300504
Keywords : continuous Archimedean triangular norm * additive generator * reconstruction * fuzzy logic * many-valued logic * conjunction
Subject RIV: BA - General Mathematics

The paper shows a direct correspondence between the first partial derivatives of a continuous Archimedean triangular norm and the first derivatives of its additive generator. An explicit formula for the additive generator is obtained. Application of the result is demonstrated on the problem of convex combinations of strict triangular norms.
Permanent Link: http://hdl.handle.net/11104/0196546