3. Mathematical Operations for Fuzzy Quantities

  1. Reinhard Viertl

Published Online: 5 JAN 2011

DOI: 10.1002/9780470974414.ch3

Statistical Methods for Fuzzy Data

Statistical Methods for Fuzzy Data

How to Cite

Viertl, R. (2011) Mathematical Operations for Fuzzy Quantities, in Statistical Methods for Fuzzy Data, John Wiley & Sons, Ltd, Chichester, UK. doi: 10.1002/9780470974414.ch3

Author Information

  1. Vienna University of Technology, Austria

Publication History

  1. Published Online: 5 JAN 2011
  2. Published Print: 11 FEB 2011

ISBN Information

Print ISBN: 9780470699454

Online ISBN: 9780470974414



  • mathematical operations for fuzzy quantities;
  • extension of algebraic operations to fuzzy numbers - and so-called extension principle from fuzzy set theory;
  • functions of fuzzy variables;
  • extension principle, natural way - in modeling propagation of imprecision;
  • addition of fuzzy numbers;
  • multiplication of fuzzy numbers;
  • mean value of fuzzy numbers - arithmetic operations for fuzzy numbers, more than two fuzzy numbers by associativity of t-norms;
  • differences and quotients;
  • fuzzy valued functions;
  • fuzzy valued functions, in environmetrics - modeling emissions to environment


This chapter contains sections titled:

  • Functions of fuzzy variables

  • Addition of fuzzy numbers

  • Multiplication of fuzzy numbers

  • Mean value of fuzzy numbers

  • Differences and quotients

  • Fuzzy valued functions

  • Problems