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The exploration of triangular norms originated from Karl Menger's work on statistical metrics, where probability distributions define distances in metric spaces. This concept led to the development of t-norms, which generalize the classical triangle inequality. Initially, the axioms for t-norms were less stringent, encompassing triangular conorms. Key contributions by Berthold Schweizer and Abe Sklar established the modern axioms for t-norms, facilitating advancements in probabilistic metric spaces and resulting in significant mathematical findings in functional equations and semigroup theory.
Buchkauf
Triangular Norms, Erich Peter Klement, R. Mesiar, E. Pap
- Sprache
- Erscheinungsdatum
- 2000
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- (Hardcover)
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- Titel
- Triangular Norms
- Sprache
- Englisch
- Autor*innen
- Erich Peter Klement, R. Mesiar, E. Pap
- Verlag
- Springer Netherlands
- Erscheinungsdatum
- 2000
- Einband
- Hardcover
- Seitenzahl
- 412
- ISBN13
- 9780792364160
- Kategorie
- Philosophie, Mathematik
- Beschreibung
- The exploration of triangular norms originated from Karl Menger's work on statistical metrics, where probability distributions define distances in metric spaces. This concept led to the development of t-norms, which generalize the classical triangle inequality. Initially, the axioms for t-norms were less stringent, encompassing triangular conorms. Key contributions by Berthold Schweizer and Abe Sklar established the modern axioms for t-norms, facilitating advancements in probabilistic metric spaces and resulting in significant mathematical findings in functional equations and semigroup theory.