Logical, Algebraic, Analytic and Probabilistic Aspects of Triangular Norms

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

· 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

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