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

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

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

Proof:

This is a consequence of Theorem 3.1.

Remark 3.6:

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

Start Free Trial

No credit card required