12. Fuzzy Arithmetic and the Extension Principle

  1. Timothy J. Ross

Published Online: 27 DEC 2010

DOI: 10.1002/9781119994374.ch12

Fuzzy Logic with Engineering Applications, Third Edition

Fuzzy Logic with Engineering Applications, Third Edition

How to Cite

Ross, T. J. (2010) Fuzzy Arithmetic and the Extension Principle, in Fuzzy Logic with Engineering Applications, Third Edition, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9781119994374.ch12

Author Information

  1. University of New Mexico, USA

Publication History

  1. Published Online: 27 DEC 2010
  2. Published Print: 15 JAN 2010

ISBN Information

Print ISBN: 9780470743768

Online ISBN: 9781119994374

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Keywords:

  • fuzzy algebraic operations;
  • fuzzy arithmetic operations;
  • Zadeh’s extension principle

Summary

This chapter shows that standard arithmetic and algebraic operations, which are based after all on the foundations of classical set theory, can be extended to fuzzy arithmetic and fuzzy algebraic operations. This extension is accomplished with Zadeh’s extension principle. The chapter uses the extension principle to perform algebraic operations on fuzzy numbers. The extension principle is one of the most basic ideas in fuzzy set theory. It provides a general method for extending crisp mathematical concepts to address fuzzy quantities, such as real algebraic operations on fuzzy numbers. These operations are computationally effective generalizations of interval analysis. The chapter presents several methods to convert extended fuzzy operations into efficient computational algorithms.

Controlled Vocabulary Terms

arithmetic codes; fuzzy logic