Logical, Algebraic, Analytic and Probabilistic Aspects of Triangular Norms

Edited by

  • Erich Klement, Johannes Kepler Universitat, Linz, Austria
  • Radko Mesiar, Slovak University of Technology, Bratislava, Slovakia

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
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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.


Book information

  • Published: March 2005
  • Imprint: ELSEVIER
  • ISBN: 978-0-444-51814-9


"...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

Table of Contents

PrefacePart I. INTRODUCTION1 Triangular norms, looking back—triangle functions, looking ahead2 Triangular norms: Basic notions and propertiesPart II. THEORETICAL ASPECTS OF TRIANGULAR NORMS3 Semigroups and triangular norms4 Generators of triangular norms5 A survey on left-continuous t-norms and pseudo t-norms6 Some aspects of functional equations7 Triangular norms on discrete settings8 Triangular norms and related operators in L*-fuzzy set theory9 Fitting triangular norms to empirical dataPart III. APPLICATIONS OF TRIANGULAR NORMS AND RELATED OPERATIONS10 Triangular norm-based mathematical fuzzy logics11 Many-valued equalities and their representations12 Varieties of algebras in fuzzy set theory13 Triangular norms and measures of fuzzy sets14 Copulas and quasi-copulas: An introduction to their properties and applications15 Transitive comparison of random variables16 Triangular norms in probabilistic metric spaces and fixed point theoryIndex