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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.
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Triangular Norms, Erich Peter Klement, R. Mesiar, E. Pap
- Language
- Released
- 2000
- product-detail.submit-box.info.binding
- (Hardcover)
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- Title
- Triangular Norms
- Language
- English
- Authors
- Erich Peter Klement, R. Mesiar, E. Pap
- Publisher
- Springer Netherlands
- Released
- 2000
- Format
- Hardcover
- Pages
- 412
- ISBN13
- 9780792364160
- Category
- Philosophy, Mathematics
- Description
- 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.