Associative Functions: Triangular Norms And Copulas

Claudi Alsina/ Maurice J Frank/ Berthold Schweizer

ISBN 10: 9812566716 / ISBN 13: 9789812566713

Edité par World Scientific Pub Co Inc, 2006

illustrated edition. 252 pages. 9.00x6.25x0.75 inches. In Stock. N° de réf. du vendeur __9812566716

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 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.

Présentation de l'éditeur: “. . . followed by a 'boom' of researches concerning associativity and its applications, among which the work of C Alsina is most remarkable. The present book, written with two collaborators, gives a proof for this statement . . . This book concludes with two appendices and an extensive bibliography. This is a marvelous book!” Mathematical Reviews “This well-written and very readable book is probably quite unique: its main subject is a single functional equation, that of associativity (joined by some more or less related equations) and several of its equations.” Zentralblatt Math 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.

Détails bibliographiques

Titre : Associative Functions: Triangular Norms And ...
Éditeur : World Scientific Pub Co Inc
Date d'édition : 2006
Reliure : Hardcover
Etat : Brand New