O'Reilly logo

Statistical Methods for Fuzzy Data by Reinhard Viertl

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

3.4 Mean value of fuzzy numbers

Arithmetic operations for fuzzy numbers can be extended to more than two fuzzy numbers by the associativity of t-norms.

This applies especially to sums of more than two fuzzy numbers.

The sum of n fuzzy numbers x1*, …, xn* is denoted by

Unnumbered Display Equation

Combining this with scalar multiplication yields the arithmetic mean of fuzzy numbers:

Unnumbered Display Equation

For the arithmetic mean of n fuzzy intervals the following proposition holds.

Proposition 3.3:

Let x1*,…,xn* be fuzzy intervals with δ-cuts Cδ(xi*) = [aδ,i; bδ,i], then the fuzzy arithmetic mean

Unnumbered Display Equation

Proof:

This is a consequence of Theorem 3.1.

Remark 3.6:

The minimum t-norm is the only combination rule for which

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required