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2007 4th International Symposium on Applied Computational Intelligence and Informatics, 2007
In this paper we completely describe all continuous migrative triangular norms. Since the migrative property excludes both idempotent and nilpotent classes, the characterization and construction is carried out by solving a functional equation for additive generators of strict t-norms.
Janos Fodor, Imre J. Rudas
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In this paper we completely describe all continuous migrative triangular norms. Since the migrative property excludes both idempotent and nilpotent classes, the characterization and construction is carried out by solving a functional equation for additive generators of strict t-norms.
Janos Fodor, Imre J. Rudas
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Triangular norms. Position paper III: continuous t-norms
Fuzzy Sets and Systems, 2004This third part of a series of position papers on triangular norms (i.e., associative, commutative binary operations in the unit interval which are non-decreasing and have 0 as a null element and 1 as a unit) receives well-known results on the representation of continuous Archimedean t-norms by means of additive generators, and the representation of ...
Klement, Erich Peter +2 more
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Order-equivalent triangular norms
Fuzzy Sets and Systems, 2015zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Kesicioğlu, M. Nesibe +2 more
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Cross-migrative triangular norms
International Journal of Intelligent Systems, 2012We study the cross-migrativity of triangular norms. The classes of continuous triangular norms, which are cross-migrative with respect to some strict or nilpotent triangular norm, respectively, are completely characterized, as well as those which are cross-migrative with respect to the greatest and smallest triangular norms, respectively.
János Fodor +2 more
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On reversible triangular norms
Fuzzy Sets and Systems, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fodor, János, Jenei, Sándor
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On continuous triangular norms
Fuzzy Sets and Systems, 1998zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jenei, Sándor, Fodor, János C.
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2003
In this chapter, we study the relationships between discrete t-norms, i.e. t-norms on a finite chain, and t-norms on the unit interval. Firstly, we investigate when and how a discrete t-norm can be extended to a (continuous) t-norm on the unit interval.
Bernard De Baets, Radko Mesiar
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In this chapter, we study the relationships between discrete t-norms, i.e. t-norms on a finite chain, and t-norms on the unit interval. Firstly, we investigate when and how a discrete t-norm can be extended to a (continuous) t-norm on the unit interval.
Bernard De Baets, Radko Mesiar
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Fuzzy Sets and Systems, 1999
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Information Sciences, 2009
A triangular norm \(T\) (a non-decreasing commutative associative binary operation on \([0,1]\) with neutral element \(e= 1\)) is extended to act on fuzzy truth values (special fuzzy subsets of \([0,1]\)) based on a (possibly different) t-norm \(T_*\).
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A triangular norm \(T\) (a non-decreasing commutative associative binary operation on \([0,1]\) with neutral element \(e= 1\)) is extended to act on fuzzy truth values (special fuzzy subsets of \([0,1]\)) based on a (possibly different) t-norm \(T_*\).
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On the order of triangular norms—comments on “A triangular norm hierarchy” by E. Cretu
Fuzzy Sets and Systems, 2002The authors present a critical overview of \textit{E. Cretu}'s paper ``A triangular norm hierarchy'' [Fuzzy Sets Syst. 120, 371-383 (2001; Zbl 0982.03014)]. They make it evident that the results on the order of t-norms (as real functions) presented by Cretu can be found in previous sources and, in a compact form, in their book [Triangular norms ...
Klement, Erich Peter +2 more
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