Triangular Norms

By: Erich Peter Klement, Radko Mesiar, Endre Pap

Write A Review

Hardcover | 31 July 2000

At a Glance

Hardcover
412 Pages

Dimensions(cm)
24.13 x 16.51 x 2.54

Hardcover

$329.75

or 4 interest-free payments of $82.44 with

or

Ships in 5 to 7 business days

The history of triangular norms started with the paper "Statistical metrics" Menger 1942]. The main idea of Karl Menger was to construct metric spaces where probability distributions rather than numbers are used in order to de- scribe the distance between two elements of the space in question. Triangular norms (t-norms for short) naturally came into the picture in the course of the generalization of the classical triangle inequality to this more general set- ting. The original set of axioms for t-norms was considerably weaker, including among others also the functions which are known today as triangular conorms. Consequently, the first field where t-norms played a major role was the theory of probabilistic metric spaces ( as statistical metric spaces were called after 1964). Berthold Schweizer and Abe Sklar in Schweizer & Sklar 1958, 1960, 1961] provided the axioms oft-norms, as they are used today, and a redefinition of statistical metric spaces given in Serstnev 1962]led to a rapid development of the field. Many results concerning t-norms were obtained in the course of this development, most of which are summarized in the monograph Schweizer & Sklar 1983]. Mathematically speaking, the theory of (continuous) t-norms has two rather independent roots, namely, the field of (specific) functional equations and the theory of (special topological) semigroups.

Industry Reviews

"The book is very well written and constitutes a valuable addition to the literature on t-norms and, in general fuzzy reasoning. It presents almost all of the most important developments of fuzzy sets and fuzzy logic by focusing on the central concept of triangular norm. It is divided into two parts and an appendix, which gives a summary of the existing families of t-norms."
(Mathematical Reviews, 2002a)

Shipping

	Standard Shipping	Express Shipping
Metro postcodes:	$9.99	$14.95
Regional postcodes:	$9.99	$14.95
Rural postcodes:	$9.99	$14.95

Orders over $79.00 qualify for free shipping.

How to return your order

At Booktopia, we offer hassle-free returns in accordance with our returns policy. If you wish to return an item, please get in touch with Booktopia Customer Care.

Additional postage charges may be applicable.

Defective items

If there is a problem with any of the items received for your order then the Booktopia Customer Care team is ready to assist you.

For more info please visit our Help Centre.

More in Combinatorics & Graph Theory

Foundations of Graph Theory - Peter Griffin

$271.99

14%
OFF

Discrete Mathematics for Data Science

Hardcover

RRP $179.00

$158.99

11%
OFF

Discrete Mathematics for Data Science

Paperback

RRP $103.00

$91.75

11%
OFF

The Random Number Code

Unlocking the Secrets of Numbers That You Can't Predict but Can Rely On

Paperback

RRP $56.99

$56.75

The Random Number Code

Unlocking the Secrets of Numbers That You Can't Predict but Can Rely On

Hardcover

RRP $399.00

$341.75

14%
OFF

Introduction to Modern Cryptography

Chapman & Hall/Crc Cryptography and Network Security

Hardcover

RRP $242.00

$233.75

Introduction to Modern Cryptography : Revised Third Edition - Jonathan Katz

$80.75

Introduction to Spectral Graph Theory : Compact Textbooks in Mathematics - Kiyan Naderi

$63.99

10%
OFF

Milestones in Graph Theory

A Century of Progress

Paperback

RRP $160.00

$154.75

$SEL PROB VIETNAMESE MATH'L..(V5) : Mathematical Olympiad - CHAU LE HAI$

SEL PROB VIETNAMESE MATH'L..(V5)

Mathematical Olympiad

Paperback

RRP $70.99

$28.00

61%
OFF

Combinatorial Problems In Mathematical Competitions

Mathematical Olympiad Series

Paperback

RRP $61.99

$55.99

10%
OFF

COMBINATORIAL EXTREMIZATION

In Mathematical Olympiad And Competitions

Paperback

RRP $45.99

$41.75

Introducing Game Theory and its Applications : Advances in Applied Mathematics - Elliott Mendelson

$73.99

10%
OFF

Handbook of Combinatorial Algebraic Geometry

Subvarieties of the Flag Variety

Hardcover

$855.75

$The Math Thought Mindset : Logic, Reasoning, and Proofs - James L. Burk$

The Math Thought Mindset

Logic, Reasoning, and Proofs

Paperback

$269.75

$The Math Thought Mindset : Logic, Reasoning, and Proofs - James L. Burk$

Acknowledgments
Introduction
Notations used in this book
Basic definitions and properties	p. 3
Algebraic aspects	p. 21
Construction of t-norms	p. 53
Families of t-norms	p. 101
Representations of t-norms	p. 121
Comparison of t-norms	p. 141
Values and discretization of t-norms	p. 157
Convergence of t-norms	p. 177
Distribution functions	p. 195
Aggregation operators	p. 215
Many-valued logics	p. 229
Fuzzy set theory	p. 249
Applications of fuzzy logic and fuzzy sets	p. 265
Generalized measures and integrals	p. 283
Families of t-norms	p. 315
Additional t-norms	p. 333
List of Figures	p. 345
List of Tables	p. 347
List of Mathematical Symbols	p. 349
Bibliography	p. 355
Index	p. 375
Table of Contents provided by Blackwell. All Rights Reserved.

Triangular Norms

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

More in Combinatorics & Graph Theory

Foundations of Graph Theory

Foundations of Graph Theory

Monomial Algebras

Chapman & Hall/CRC Monographs and Research Notes in Mathematics

Discrete Mathematics for Data Science

Discrete Mathematics for Data Science

The Random Number Code

Unlocking the Secrets of Numbers That You Can't Predict but Can Rely On

The Random Number Code

Unlocking the Secrets of Numbers That You Can't Predict but Can Rely On

Introduction to Modern Cryptography

Chapman & Hall/Crc Cryptography and Network Security

Introduction to Modern Cryptography

Revised Third Edition

Mathematics of Tabletop Games

AK Peters/CRC Recreational Mathematics

A First Look At Graph Theory

Introduction to Spectral Graph Theory

Compact Textbooks in Mathematics

Principles And Techniques In Combinatorics

Milestones in Graph Theory

A Century of Progress

SEL PROB VIETNAMESE MATH'L..(V5)

Mathematical Olympiad

Combinatorial Problems In Mathematical Competitions

Mathematical Olympiad Series

COMBINATORIAL EXTREMIZATION

In Mathematical Olympiad And Competitions

Introducing Game Theory and its Applications

Advances in Applied Mathematics

PRINCIPLES AND TECHNIQUES IN COMBINATORICS

SOLUTIONS MANUAL

Handbook of Combinatorial Algebraic Geometry

Subvarieties of the Flag Variety

The Math Thought Mindset

Logic, Reasoning, and Proofs

The Math Thought Mindset

Logic, Reasoning, and Proofs

A Tour through Graph Theory

Textbooks in Mathematics

A Tour through Graph Theory

Textbooks in Mathematics

This product is categorised by