| Triangular Norms Softcover Repri Edition Contributor(s): Klement, Erich Peter (Author), Mesiar, R. (Author), Pap, E. (Author) |
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ISBN: 904815507X ISBN-13: 9789048155071 Publisher: Springer OUR PRICE: $208.99 Product Type: Paperback - Other Formats Published: December 2010 |
| Additional Information |
| BISAC Categories: - Philosophy | Logic - Mathematics | Algebra - Abstract - Mathematics | Logic |
| Dewey: 515.724 |
| Series: Trends in Logic |
| Physical Information: 0.84" H x 6.14" W x 9.21" (1.25 lbs) 387 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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. |