独立模糊随机变量的强大数律

Strong Law of Large Numbers of Fuzzy Random Variables

设{xn,n≥1}是一模糊随机变量序列且{an,n≥1}是一列常数,且满足0<an↑∞.设函数满足于φ(x)↑,φ(x)x↑,φx(2x)↓,如果有n∞=1Σni=1ΣE(φ(‖xi‖ρp))φ(an)<∞,∞n=1Σ(ni=1ΣE(‖xi‖ρ2p)an2)s<∞,则E‖xi‖ρ2p/an→0等价ni=1ΣXi/an→C 0-等价ni=1ΣXi/an→a.s.0-等价ni=1ΣXi/an→p 0-.

Let {x,n ≥ 1} be a sequence of independent fuzzy random variables and {a,n ≥ 1} sequence of positive real numbers converging to ∞.In this paper we show that φ（x）↑,↑,↓ under the assumption with some restrictions on n∞=1Σni=1ΣE（φ（‖xi‖ρp））φ（an）∞,∞n=1Σ（ni=1ΣE（‖xi‖ρ2p）an2）s∞. If and only if E‖xi‖ρ2p/an→0 If and only if ni=1ΣXi/an→C 0-If and only if ni=1ΣXi/an→a.s.0-If and only if ni=1ΣXi/an→p 0-.