Description

This volume gives a state of the art of triangular norms which can be used for the generalization of several mathematical concepts, such as conjunction, metric, measure, etc. 16 chapters written by leading experts provide a state of the art overview of theory and applications of triangular norms and related operators in fuzzy logic, measure theory, probability theory, and probabilistic metric spaces. Key Features: - Complete state of the art of the importance of triangular norms in various mathematical fields - 16 self-contained chapters with extensive bibliographies cover both the theoretical background and many applications - Chapter authors are leading authorities in their fields - Triangular norms on different domains (including discrete, partially ordered) are described - Not only triangular norms but also related operators (aggregation operators, copulas) are covered - Book contains many enlightening illustrations

Key Features

· Complete state of the art of the importance of triangular norms in various mathematical fields · 16 self-contained chapters with extensive bibliographies cover both the theoretical background and many applications · Chapter authors are leading authorities in their fields · Triangular norms on different domains (including discrete, partially ordered) are described · Not only triangular norms but also related operators (aggregation operators, copulas) are covered · Book contains many enlightening illustrations

Readership

Mathematical and Computer Science Libraries, Scholars and students in mathematics and computer science with a particular interest in many-valued logic, its algebraic and analytical features, and in uncertainty modelling.

Table of Contents

Preface Part I. INTRODUCTION 1 Triangular norms, looking back—triangle functions, looking ahead 2 Triangular norms: Basic notions and properties Part II. THEORETICAL ASPECTS OF TRIANGULAR NORMS 3 Semigroups and triangular norms 4 Generators of triangular norms 5 A survey on left-continuous t-norms and pseudo t-norms 6 Some aspects of functional equations 7 Triangular norms on discrete settings 8 Triangular norms and related operators in L*-fuzzy set theory 9 Fitting triangular norms to empirical data Part III. APPLICATIONS OF TRIANGULAR NORMS AND RELATED OPERATIONS 10 Triangular norm-based mathematical fuzzy logics 11 Many-valued equalities and their representations 12 Varieties of algebras in fuzzy set theory 13 Triangular norms and measures of fuzzy sets 14 Copulas and quasi-copulas: An introduction to their properties and applications 15 Transitive comparison of random variables 16 Triangular norms in probabilistic metric spaces and fixed point theory Index

Details

No. of pages:
492
Language:
English
Copyright:
© 2005
Published:
Imprint:
Elsevier Science
Electronic ISBN:
9780080459530
Print ISBN:
9780444518149
Print ISBN:
9780444545794

About the editors

Reviews

"...very good information about the state of the art of the triangular norms theory in the recent time. This quality makes the volume very attractive for everybody who is interested in the t-norms in the models of uncertainty." -Milan Mares, in BOOK REVIEWS, Vol. 41, 2005