Triangular Norms [electronic resource] /

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.

Bibliographic Details

Main Authors:	Klement, Erich Peter. author., Mesiar, Radko. author., Pap, Endre. author., SpringerLink (Online service)
Format:	Texto biblioteca
Language:	eng
Published:	Dordrecht : Springer Netherlands : Imprint: Springer, 2000
Subjects:	Philosophy., Logic., Algebra., Ordered algebraic structures., Mathematical logic., Order, Lattices, Ordered Algebraic Structures., Mathematical Logic and Foundations.,
Online Access:	http://dx.doi.org/10.1007/978-94-015-9540-7
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