This work proposes the concept of uncorrelation for fuzzy random variables, which is weaker than independence. For the sequence of uncorrelated fuzzy random variables, weak and strong laws of large numbers are studied under the uniform Hausdorff metric . The results generalize the law of large numbers for independent fuzzy random variables.
AhmadzadeH., AminiM., TaheriS.M. and BozorgniaA., Some probabilistic inequalities for fuzzy random variables, Iranian Journal of Fuzzy Systems14(6) (2017), 119–134.
2.
ArtsteinZ. and VitaleR.A., A strong law of large numbers for random compact sets, Ann. Probab3 (1975), 879–882.
3.
AumannR., Integrals of set-valued functions, J Math Anal Appl12 (1965), 1–12.
4.
FuK.A. and ZhangL.X., Strong laws of large numbers for arrays of row wise independent random compact sets and fuzzy random sets, Fuzzy Sets and Systems159(24) (2008), 3360–3368.
5.
GuanL. and LiS., Laws of large numbers for weighted sums of fuzzyset-valued random variables, Inter. J. of Uncertainty, Fuzziness and Knowledge-based System12 (2004), 811–825.
6.
GuanL., LiS. and InoueH., Strong laws of large numbers for weighted sums of set-valued random variables in Rademacher type pBanach space, Scientiae Mathematicae Japonicae67(3) (2007), 377–392.
7.
GuanL. and ZhangJ., Laws of Large Numbers for Uncorrelated Set-Valued Random Variables, arXiv:2011.07199 [math.PR] (2020).
8.
HiaiF., Convergence of conditional expectations and strong laws of large numbers for multivalued random variables, Trans. A.M.S.291 (1985), 613–627.
9.
HiaiF. and UmegakiH., Integrals, conditional expectations and martingales of multivalued functions, Jour Multivar Anal7 (1977), 149–182.
10.
HongD.H., Strong laws of large numbers for t-norm-based addition of fuzzy set-valued random variables, Fuzzy Sets and Systems223 (2013), 26–38.
11.
HongD.H., The law of large numbers and renewal process forT-related weighted fuzzy numbers on , Information Sciences228 (2013), 45–60.
12.
InoueH., A strong law of large numbers for fuzzy random sets, Fuzzy Sets and Systems41 (1991), 285–291.
13.
KimY.K., A strong law of large numbers for fuzzy random variables, Fuzzy Sets and Systems111 (2000), 319–323.
14.
KimY.K., Weak laws of large numbers for weighted sums of fuzzy random variables, International Journal of Fuzzy Logic and Intelligent Systems13(3) (2013), 215–223.
15.
KlementE.P., PuriM.L. and RalescuD.A., Limit theorems for fuzzy random variables, Proc. Roy. Soc. Lond. A.407 (1986), 171–182.
16.
LiS. and OguraY., Fuzzy random variables, conditional expectations and fuzzy martingales, J Fuzzy Math4 (1996), 905–927.
17.
LiS. and OguraY., Strong laws of numbers for independent fuzzy set-valued random variables, Fuzzy Sets and Systems157(2006), 2569–2578.
18.
LiS., OguraY. and KreinovichV., Limit Theorems and Applications of Set-Valued and Fuzzy Sets-Valued Random Variables, Kluwer Academic Publishers (2002).
19.
MolchanovI.S., On strong laws of large numbers for random upper semi continuous functions, Fuzzy Sets and Systems235(1999), 349–355.
20.
ProskeF.N. and PuriM.L., Strong law of large numbers for Banach space valued fuzzy random variables, Journal of Theoretical Probability15(2) (2002), 543–551.
21.
ProskeF.N. and PuriM.L., A strong law of large numbers for generalized random sets from the view point of empirical processes, Proc Amer Math Soc131(9) (2003), 2937–2944.
22.
PuriM.L. and RalescuD.A., Fuzzy random variables, J Math AnalAppl114 (1986), 406–422.
23.
QuangN.V. and ThuanN.T., Strong laws of large numbers for adapted arrays of set-valued and fuzzy-valued random variables in banach space, Fuzzy Sets and Systems209 (2012), 14–32.
24.
TaylorR.L., SeymourL. and ChenY., Weak law of large numbers for fuzzy random sets, Nonlinear Anal47 (2001), 1245–1256.
25.
TeránP., Strong law of large numbers for t-normed arithmetics, Fuzzy Sets and Systems159 (2008), 343–360.
26.
UemuraT., A law of large numbers for random sets, Fuzzy Sets and Systems59 (1993), 181–188.
