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Book synopsis

The functional equation of associativity is the topic of Abel's first contribution to Crelle's Journal. Seventy years later, it was featured as the second part of Hilbert's Fifth Problem, and it was solved under successively weaker hypotheses by Brouwer (1909), Cartan (1930) and Aczel (1949). In 1958, B Schweizer and A Sklar showed that the "triangular norms" introduced by Menger in his definition of a probabilistic metric space should be associative; and in their book Probabilistic Metric Spaces, they presented the basic properties of such triangular norms and the closely related copulas. Since then, the study of these two classes of functions has been evolving at an ever-increasing pace and the results have been applied in fields such as statistics, information theory, fuzzy set theory, multi-valued and quantum logic, hydrology, and economics, in particular, risk analysis. This book presents the foundations of the subject of associative functions on real intervals. It brings togethe

Book details

Book category Books in English Mathematics & science Mathematics Calculus & mathematical analysis

• Full title: Associative Functions: Triangular Norms And Copulas
• Author: Claudi Alsina, Maurice J. Frank, Berthold Schweizer
• Language: English
• Binding: Hardback
• Number of pages: 252
• EAN: 9789812566713
• ISBN: 9812566716
• ID: 05068254
• Publisher: World Scientific Publishing Co Pte Ltd
• Weight: 564 g
• Dimensions: 233 × 164 × 21 mm
• Date of publishing: 23. February 2006

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