ISBN: 9789401595407

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 rath… Meer...

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.; PDF; Politics, Philosphy & Religion > Philosophy > Philosophy: logic, Springer Netherlands<

ISBN: 9789401595407

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 rat… Meer...

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., Springer<

ISBN: 9789401595407

*Triangular Norms* / pdf eBook für 213.99 € / Aus dem Bereich: eBooks, Fachthemen & Wissenschaft, Philosophie Medien > Bücher nein eBook als pdf eBooks > Fachthemen & Wissenschaft > Philo… Meer...

*Triangular Norms* / pdf eBook für 213.99 € / Aus dem Bereich: eBooks, Fachthemen & Wissenschaft, Philosophie Medien > Bücher nein eBook als pdf eBooks > Fachthemen & Wissenschaft > Philosophie, Springer Netherlands<

ISBN: 9789401595407

Triangular Norms: ab 213.99 € eBooks > Fachthemen & Wissenschaft > Philosophie Springer Netherlands eBook als pdf, Springer Netherlands

2013, ISBN: 9789401595407

eBooks, eBook Download (PDF), [PU: Springer Netherlands], Springer Netherlands, 2013