Triangular Norms - Couverture souple

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

Couverture souple

ISBN 10 : 904815507X ISBN 13 : 9789048155071

Editeur : Springer, 2010

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.

Détails de l'édition

• Éditeur: Springer
• Date d'édition: 2010
• Langue: anglais
• ISBN 10: 904815507X
• ISBN 13: 9789048155071
• Reliure: Broché
• Nombre de pages: 412
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