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Associative Functions: Triangular Norms And Copulas [Hardcover]

By Claudi Alsina (Author), Maurice J Frank (Author) & Berthold Schweizer (Author)
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Item description for Associative Functions: Triangular Norms And Copulas by Claudi Alsina, Maurice J Frank & Berthold Schweizer...

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 together results that have been widely scattered in the literature and adds much new material. In the process, virtually all the standard techniques for solving functional equations in one and several variables come into play. Thus, the book can serve as an advanced undergraduate or graduate text on functional equations.

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Item Specifications...

Studio: World Scientific Publishing Company
Pages   252
Est. Packaging Dimensions:   Length: 8.98" Width: 6.14" Height: 0.87"
Weight:   1.28 lbs.
Binding  Hardcover
Release Date   Feb 22, 2006
Publisher   World Scientific Publishing Company
ISBN  9812566716  
ISBN13  9789812566713  

Availability  0 units.

More About Claudi Alsina, Maurice J Frank & Berthold Schweizer

Register your artisan biography and upload your photo! Claudi Alsina received his B.A. and Ph.D. in mathematics from the University of Barcelona. His post-doctoral studies were at the University of Massachusetts, Amherst. He is Professor of Mathematics at the Technical University of Catalonia and has developed a wide range of international activities, research papers, publications and hundreds of lectures on mathematics and mathematics education. His latest books include Associative Functions: Triangular Norms and Copulas with M. J. Frank and B. Schweizer, WSP, 2006; Math Made Visual. Creating Images for Understanding Mathematics with Roger B. Nelsen, MAA, 2006; Vitaminas Matematicas and El Club de la Hipotenusa, Ariel, 2008.

Claudi Alsina has an academic affiliation as follows - Universitat Politecnica de Catalunya, Barcelona Universitat Polit??cni.

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Product Categories

1Books > Subjects > Professional & Technical > Professional Science > Mathematics > Applied > General
2Books > Subjects > Professional & Technical > Professional Science > Mathematics > Mathematical Analysis
3Books > Subjects > Science > General
4Books > Subjects > Science > Mathematics > Applied > General
5Books > Subjects > Science > Mathematics > Applied
6Books > Subjects > Science > Mathematics > General
7Books > Subjects > Science > Mathematics > Mathematical Analysis

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