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Author Alsina, Claudi.

Title Associative functions : triangular norms and copulas / Claudi Alsina, Maurice J. Frank, Berthold Schweizer.

Publication Info. Hackensack, NJ : World Scientific, [2006]
©2006

Item Status

Description 1 online resource (xiv, 237 pages) : illustrations
Physical Medium polychrome
Description text file
Bibliography Includes bibliographical references (pages 223-234) and index.
Summary The dynamics of complex systems can clarify the creation of structures in Nature. This creation is driven by the collective interaction of constitutive elements of the system. Such interactions are frequently nonlinear and are directly responsible for the lack of prediction in the evolution process. The self-organization accompanying these processes occurs all around us and is constantly being rediscovered, under the guise of a new jargon, in apparently unrelated disciplines. This volume offers unique perspectives on aspects of fractals and complexity and, through the examination of complementary techniques, provides a unifying thread in this multidisciplinary endeavour. Do nonlinear interactions play a role in the complexity management of socio-economic-political systems? Is it possible to extract the global properties of genetic regulatory networks without knowing the details of individual genes? What can one learn by transplanting the self-organization effects known in laser processes to the study of emotions? What can the change in the level of complexity tell us about the physiological state of the organism? The reader will enjoy finding the answers to these questions and many more in this book.
Contents Preface -- Special symbols -- 1. Introduction. 1.1. Historical notes. 1.2. Preliminaries. 1.3. t-norms and s-norms. 1.4. Copulas -- 2. Representation theorems for associative functions. 2.1. Continuous, Archimedean t-norms. 2.2. Additive and multiplicative generators. 2.3. Extension to arbitrary closed intervals. 2.4. Continuous, non-Archimedean t-norms. 2.5. Non-continuous t-norms. 2.6. Families of t-norms. 2.7. Other representation theorems. 2.8. Related functional equations -- 3. Functional equations involving t-norms. 3.1. Simultaneous associativity. 3.2. n-duality. 3.3. Simple characterizations of Min. 3.4. Homogeneity. 3.5. Distributivity. 3.6. Conical t-norms. 3.7. Rational Archimedean t-norms. 3.8. Extension and sets of uniqueness -- 4. Inequalities involving t-norms. 4.1. Notions of concavity and convexity. 4.2. The dominance relation. 4.3. Uniformly close associative functions. 4.4. Serial iterates and n-copulas. 4.5. Positivity.
Local Note eBooks on EBSCOhost EBSCO eBook Subscription Academic Collection - North America
Subject Functional equations.
Functional equations.
Associative law (Mathematics)
Associative law (Mathematics)
Mathematical analysis.
Mathematical analysis.
Functional equations -- Study and teaching -- Textbooks.
Genre/Form Textbooks.
Subject Associative law (Mathematics) -- Study and teaching -- Textbooks.
Mathematical analysis -- Study and teaching -- Textbooks.
Mathematical analysis -- Study and teaching.
Genre/Form Electronic books.
Textbooks.
Added Author Schweizer, B. (Berthold)
Frank, Maurice J.
Other Form: Print version: Alsina, Claudi. Associative functions. Hackensack, NJ : World Scientific, ©2006 9812566716 9789812566713 (DLC) 2006284938 (OCoLC)76144355
ISBN 9789812774200 (electronic book)
9812774203 (electronic book)
1281919349
9781281919342