Book Cover
Book
Author Alsina, Claudi.

Title Associative functions : triangular norms and copulas / Claudi Alsina, Maurice J. Frank, Berthold Schweizer
Published Hackensack, NJ : World Scientific, [2006]
©2006

Copies

Location Call no. Vol. Availability
 MELB  515.75 Als/Aft  AVAILABLE
Description xiv, 237 pages : illustrations ; 24 cm
Contents Machine derived contents note: 1. Introduction 1 -- 1.1 Historical notes 1 -- 1.2 Preliminaries 6 -- 1.3 t-norms and s-norms 9 -- 1.4 Copulas 17 -- 2. Representation theorems for associative functions 23 -- 2.1 Continuous, Archimedean t-norms 23 -- 2.2 Additive and multiplicative generators 38 -- 2.3 Extension to arbitrary closed intervals 51 -- 2.4 Continuous, non-Archimedean t-norms 57 -- 2.5 Non-continuous t-norms 64 -- 2.6 Families of t-norms 70 -- 2.7 Other representation theorems 81 -- 2.8 Related functional equations. 93 -- 3. Functional equations involving t-norms 99 -- 3.1 Simultaneous associativity 99 -- 3.2 n-duality 110 -- 3.3 Simple characterizations of Min 127 -- 3.4 Homogeneity 129 -- 3.5 Distributivity 134 -- 3.6 Conical t-norms 137 -- 3.7 Rational Archimedean t-norms 143 -- 3.8 Extension and sets of uniqueness 151 -- 4. Inequalities involving t-norms 173 -- 4.1 Notions of concavity and convexity 173 -- 4.2 The dominance relation 182 -- 4.3 Uniformly close associative functions 189 -- 4.4 Serial iterates and n-copulas 194 -- 4.5 Positivity 203
Summary "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."--BOOK JACKET
Bibliography Includes bibliographical references (pages 223-234) and index
Subject Associative law (Mathematics)
Associative law (Mathematics) -- Study and teaching -- Textbooks.
Functional equations -- Study and teaching -- Textbooks.
Functional equations.
Mathematical analysis -- Study and teaching -- Textbooks.
Mathematical analysis.
Genre/Form Textbooks.
Author Frank, Maurice J.
Schweizer, B. (Berthold)
LC no. 2006284938
ISBN 9812566716