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

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