Logical, algebraic, analytic, and probabilistic aspects of triangular norms / edited by Erich Peter Klement, Radko Mesiar.

Format:

Book

Contributor:

Klement, E. P. (Erich Peter)

Mesiar, Radko

Anne and Joseph Trachtman Memorial Book Fund.

Language:

English

Subjects (All):

Fuzzy sets.

Set theory.

Physical Description:

viii, 481 pages : illustrations ; 25 cm

Edition:

First edition.

Place of Publication:

Amsterdam ; Boston : Elsevier, 2005.

Summary:

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. 7 Complete state of the art of the importance of triangular norms in various mathematical fields 7 16 self-contained chapters with extensive bibliographies cover both the theoretical background and many applications 7 Chapter authors are leading authorities in their fields 7 Triangular norms on different domains (including discrete, partially ordered) are described 7 Not only triangular norms but also related operators (aggregation operators, copulas) are covered 7 Book contains many enlightening illustrations

Contents:

1 Triangular norms, looking back-triangle functions, looking ahead / Berthold Schweizer 3

2 Triangular norms: Basic notions and properties / Erich Peter Klement, Radko Mesiar, Endre Pap 17

Part II Theoretical Aspects of Triangular Norms

3 Semigroups and triangular norms / Erich Peter Klement, Radko Mesiar, Endre Pap 63

4 Generators of triangular norms / Andrea Mesiarova 95

5 A survey on left-continuous t-norms and pseudo t-norms / Sandor Jenei 113

6 Some aspects of functional equations / Wolfgang Sander 143

7 Triangular norms on discrete settings / Gaspar Mayor, Joan Torrens 189

8 Triangular norms and related operators in L*-fuzzy set theory / Glad Deschrijver, Etienne E. Kerre 231

9 Fitting triangular norms to empirical data / Gleb Beliakov 261

Part III Applications of Triangular Norms and Related Operations

10 Triangular norm-based mathematical fuzzy logics / Siegfried Gottwald, Petr Hajek 275

11 Many-valued equalities and their representations / Ulrich Hohle 301

12 Varieties of algebras in fuzzy set theory / Guram Bezhanishvili, Mai Gehrke, John Harding, Carol Walker, Elbert Walker 321

13 Triangular norms and measures of fuzzy sets / Mirko Navara 345

14 Copulas and quasi-copulas: An introduction to their properties and applications / Roger B. Nelsen 391

15 Transitive comparison of random variables / Bernard De Baets, Hans De Meyer, Bart De Schuymer 415

16 Triangular norms in probabilistic metric spaces and fixed point theory / Olga Hadzic, Endre Pap 443.

Notes:

Includes bibliographical references and index.

Local Notes:

Acquired for the Penn Libraries with assistance from the Anne and Joseph Trachtman Memorial Book Fund.

ISBN:

0444518142

OCLC:

57465745