Triangular Norms (Trends in Logic)

Klement, Erich Peter Peter; Mesiar, R.; Pap, E.

ISBN 10: 904815507X / ISBN 13: 9789048155071

Edité par Springer, 2010

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N° de réf. du vendeur ria9789048155071_new

Détails bibliographiques

• Titre: Triangular Norms (Trends in Logic)
• Éditeur: Springer
• Date de parution: 2010
• Langue: anglais
• ISBN à 10 chiffres: 904815507X
• ISBN à 13 chiffres: 9789048155071
• Reliure: Couverture souple
• État de l'article: New

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Synopsis

The history of triangular norms started with the paper "Statistical metrics" [Menger 1942]. The main idea of Karl Menger was to construct metric spaces where probability distributions rather than numbers are used in order to de- scribe the distance between two elements of the space in question. Triangular norms (t-norms for short) naturally came into the picture in the course of the generalization of the classical triangle inequality to this more general set- ting. The original set of axioms for t-norms was considerably weaker, including among others also the functions which are known today as triangular conorms. Consequently, the first field where t-norms played a major role was the theory of probabilistic metric spaces ( as statistical metric spaces were called after 1964). Berthold Schweizer and Abe Sklar in [Schweizer & Sklar 1958, 1960, 1961] provided the axioms oft-norms, as they are used today, and a redefinition of statistical metric spaces given in [Serstnev 1962]led to a rapid development of the field. Many results concerning t-norms were obtained in the course of this development, most of which are summarized in the monograph [Schweizer & Sklar 1983]. Mathematically speaking, the theory of (continuous) t-norms has two rather independent roots, namely, the field of (specific) functional equations and the theory of (special topological) semigroups.