ویراساینس.
سند علمی

On law of large numbers for L-R fuzzy numbers∗

Robert Fullér

چکیده

This paper extends the author’s earlier work on the Law of Large Numbers for fuzzy numbers [2] to the case where the fuzzy numbers are of type L-R. Namely, we shall define a class of Archimedean triangular norms in which the equality lim n→∞ Nes(mn − ≤ ηn ≤ mn + = 1, for any > 0, holds for all sequences of fuzzy numbers, ξi = (Mi, α, β)LR, i ∈ N, with twice differentiable and concave shape functions L and R; where ηn = ξ1 ⊕ · · · ⊕ ξn n , n ∈ N, is the sequence of t-arithmetic means of the first n-terms of {ξi} (defined via a sup-t-norm convolution), mn = M1 + · · · + Mn n , and Nes denotes Necessity.

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