Explicit Formulas for Generators of Triangular Norms

0341931 - ÚI 2011 RIV HU eng J - Journal Article
Navara, M. - Petrík, Milan - Sarkoci, P.
Explicit Formulas for Generators of Triangular Norms.
Publicationes Mathematicae-Debrecen. Roč. 77, 1-2 (2010), s. 171-191. ISSN 0033-3883
Grant - others:GA ČR(CZ) GA201/07/1136
Institutional research plan: CEZ:AV0Z10300504
Keywords : continuous Archimedean triangular norm * additive generator * multiplicative generator
Subject RIV: BA - General Mathematics
Impact factor: 0.568, year: 2010

Triangular norms are associative operations which represent conjunctions in fuzzy logic. They were also studied in the context of probabilistic metric spaces. It is known that each continuous Archimedean triangular norm can be determined by additive and multiplicative generators. However, finding a generator of a given triangular norm may be a difficult task. The geometry of the generator does not seem to reflect the properties of the triangular norm in an intuitive way. We show that this need not be the case for a large class of triangular norms which allow to reconstruct the generators from partial derivatives of triangular norms. This class is broad enough to cover all continuous Archimedean triangular norms which we found in the literature.
Permanent Link: http://hdl.handle.net/11104/0184773