Skip to main content

Triangular Norms

  • Book
  • © 2000


Part of the book series: Trends in Logic (TREN, volume 8)

This is a preview of subscription content, log in via an institution to check access.

Access this book

eBook USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

About this book

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.

Similar content being viewed by others


Table of contents (14 chapters)

  1. Part I

  2. Part II


"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)

Authors and Affiliations

  • Johannes Kepler University, Linz, Austria

    Erich Peter Klement

  • Slovak University of Technology, Bratislava, Slovakia

    Radko Mesiar

  • Czech Academy of Sciences, Prague, Czech Republic

    Radko Mesiar

  • University of Novi Sad, Yugoslavia

    Endre Pap

Bibliographic Information

  • Book Title: Triangular Norms

  • Authors: Erich Peter Klement, Radko Mesiar, Endre Pap

  • Series Title: Trends in Logic

  • DOI:

  • Publisher: Springer Dordrecht

  • eBook Packages: Springer Book Archive

  • Copyright Information: Springer Science+Business Media Dordrecht 2000

  • Hardcover ISBN: 978-0-7923-6416-0Published: 31 July 2000

  • Softcover ISBN: 978-90-481-5507-1Published: 07 December 2010

  • eBook ISBN: 978-94-015-9540-7Published: 17 April 2013

  • Series ISSN: 1572-6126

  • Series E-ISSN: 2212-7313

  • Edition Number: 1

  • Number of Pages: XIX, 387

  • Topics: Logic, Order, Lattices, Ordered Algebraic Structures, Mathematical Logic and Foundations

Publish with us