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.
Let x1*,…,xn* be fuzzy intervals with δ-cuts Cδ(xi*) = [aδ,i; bδ,i], then the fuzzy arithmetic mean
This is a consequence of Theorem 3.1.
The minimum t-norm is the only combination rule for which