Geodesic
Maximal inequalities and some convergence theorems for fuzzy random variables
Kybernetika, Tome 52 (2016) no. 2, pp. 307-328 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Some maximal inequalities for quadratic forms of independent and linearly negative quadrant dependent fuzzy random variables are established. Strong convergence of such quadratic forms are proved based on the martingale theory. A weak law of large numbers for linearly negative quadrant dependent fuzzy random variables is stated and proved.
Some maximal inequalities for quadratic forms of independent and linearly negative quadrant dependent fuzzy random variables are established. Strong convergence of such quadratic forms are proved based on the martingale theory. A weak law of large numbers for linearly negative quadrant dependent fuzzy random variables is stated and proved.
DOI : 10.14736/kyb-2016-2-0307
Classification : 60F05, 60F15
Keywords: fuzzy random variable; quadratic form; linearly negative quadrant dependence; law of large numbers; almost surely convergence 
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Ahmadzade, Hamed; Amini, Mohammad; Taheri, Seyed Mahmoud; Bozorgnia, Abolghasem. Maximal inequalities and some convergence theorems for fuzzy random variables. Kybernetika, Tome 52 (2016) no. 2, pp. 307-328. doi: 10.14736/kyb-2016-2-0307

[1] Ahmadzade, H., Amini, M., Taheri, S. M., Bozorgnia, A.: Some limit theorems for independent fuzzy random variables. Thaiwan J. Math. 12 (2014), 537-548. | MR | Zbl

[2] Ahmadzade, H., Amini, M., Taheri, S. M., Bozorgnia, A.: Some moment inequalities for fuzzy martingales and their applications. J. Uncertainty Anal. Appl. 2 (2014), 1-14. | DOI

[3] Aumann, R. J.: Integrals of set-valued functions. J. Math. Anal. Appl. 12 (1965), 1-12. | DOI | MR | Zbl

[4] Cuzich, J., Gine, E., Zinn, J.: Laws of large numbers for quadratic forms, maxima of products and truncated sums of i.i.d. random variables. Ann. Probab. 23 (1995), 292-333. | DOI | MR

[5] Eghbal, N., Amini, M., Bozorgnia, A.: Some maximal inequalities for quadratic forms of negative superadditive dependence random variables. Stat. Probab. Lett. 80 (2010), 587-591. | DOI | MR | Zbl

[6] Eghbal, N., Amini, M., Bozorgnia, A.: On the Kolmogorov inequalities for quadratic forms of dependent uniformly bounded random variables. Stat. Probab. Lett. 81 (2011), 1112-1120. | DOI | MR | Zbl

[7] Fei, W.: Regularity and stopping theorem for fuzzy martingales with continuous parameters. Inform. Sci. 169 (2005), 175-87. | DOI | MR | Zbl

[8] Fei, W., Wu, R., Shao, S.: Doobs stopping theorem for fuzzy (super, sub) martingales with discrete time. Fuzzy Set. Syst. 135 (2003), 377-390. | DOI | MR | Zbl

[9] Feng, Y.: Convergence theorems for fuzzy random variables and fuzzy martingales. Fuzzy Set. Syst. 103 (1999), 435-441. | DOI | MR | Zbl

[10] Feng, Y.: An approach to generalize laws of large numbers for fuzzy random variables. Fuzzy Set. Syst. 128 (2002), 237-245. | DOI | MR | Zbl

[11] Feng, Y., Hu, L., Shu, H.: The variance and covariance of fuzzy random variables and their applications. Fuzzy Set. Syst. 120 (2001), 487-497. | MR | Zbl

[12] Fu, Y., Wu, Q.: Almost sure central limit theoremfor LNQD sequences. J. Guilin University of Technology 30 (2010), 4, 637-639. | DOI

[13] Fu, K., Zhang, L.-X.: Strong limit theorems for random sets and fuzzy random sets with slowly varying weights. Inform. Sci. 178 (2008), 2648-2660. | DOI | MR | Zbl

[14] Gadidov, A.: Strong law of large numbers for multilinear forms. Ann. Probab. 26 (1998), 902-923. | DOI | MR | Zbl

[15] Gut, A.: Probability: A Graduate Course. Springer, New York 2005. | DOI | MR | Zbl

[16] Hoeffding, W.: Masstabinvariante Korrelationstheorie. Schriften des Matematischen Instituts und des Instituts fur Angewandte Mathematik der Universitat 1940.

[17] Hong, D.: A convergence of fuzzy random variables. Kybernetika 39 (2003), 275-280. | MR | Zbl

[18] Hong, D., Kim, K.: Weak law of large number for i.i.d. fuzzy random variables. Kybernetika 43 (2007), 87-96. | MR

[19] Joo, S. Y., Kim, Y. K., Kwon, J S.: On Chung's type law of large numbers for fuzzy random variables. Stat. Prob. Lett. 74 (2005), 67-75. | DOI | MR | Zbl

[20] Klement, E. P., Puri, M. L., Ralescu, D. A.: Limit theorems for fuzzy random variables. Proc. Roy. Soc. London Ser. A 407 (1986), 171-182. | DOI | MR | Zbl

[21] Ko, M. H., Choi, Y. K., Choi, Y.-S.: Exponential probability inequality for linearly negative quadrant dependent random variables. Korean Math. Soc. Comm. 22 (2007), 1, 137-143. | DOI | MR | Zbl

[22] Korner, R.: On the variance of fuzzy random variables. Fuzzy Set. Syst. 92 (1997), 83-93. | DOI | MR | Zbl

[23] Kwakernaak, H.: Fuzzy random variables I. | Zbl

[24] Miranda, E., Couso, I., Gil, P.: Random sets as imprecise random variables. J. Math. Anal. Appl. 307 (2005), 32-47. | DOI | MR | Zbl

[25] Miyakoshi, M., Shimbo, M.: A strong law of large numbers for fuzzy random variables. Fuzzy Set. Syst. 12 (1984), 133-142. | DOI | MR | Zbl

[26] Moore, R. E., Kearfott, R. B., Cloud, M. J.: Introduction to Interval Analysis. SIAM, Philadelphia 2009. | DOI | MR | Zbl

[27] Newman, C. M.: Asymptotic independence and limit theorems for positively and negatively dependent random variables. Statist. Probab. 5 (1984), 127-140. | DOI | MR

[28] Nguyen, H. T.: A note on the extension principle for fuzzy sets. J. Math. Anal. Appl. 64 (1978), 369-380. | DOI | MR | Zbl

[29] Parchami, A., Mashinchi, M., Partovinia, V.: A consistent confidence interval for fuzzy capability index. Appl. Comput. Math. 7 (2008), 119-125. | MR

[30] Puri, M. L., Ralescu, D. A.: Fuzzy random variables. J. Math. Anal. Appl. 114 (1986), 402-422. | DOI | MR | Zbl

[31] Puri, M. L., Ralescu, D. A.: Convergence theorem for fuzzy martingales. J. Math. Anal. Appl. 160 (1991), 107-122. | DOI | MR | Zbl

[32] Ralescu, D. A.: Fuzzy random variables revisited. In: Math. Fuzzy Sets, Handbook Fuzzy Sets, Series 3 Kluwer, Boston 1999, pp. 701-710. | DOI | MR | Zbl

[33] Sadeghpour-Gildeh, B., Gien, D.: La distance-$D_{p,q}$ et le coeffcient de corrélation entre deux variables aléatoires floues. Actes de LFA'01, Monse-Belgium 2001, pp. 97-102.

[34] Shanchao, Y.: Moment inequalities for sums of products of independent random variables. Stat. Probab. Lett. 76 (2006), 1994-2000. | DOI | MR | Zbl

[35] Stojakovic, M.: Fuzzy martingalesa simple form of fuzzy processes. Stochast. Anal. Appl. 14 (1996), 3, 355-367. | DOI | MR

[36] Taylor, R. L., Seymour, L., Chen, Y.: Weak laws of large numbers for fuzzy random sets. Nonlinear Anal. 47 (2001), 1245-125. | DOI | MR | Zbl

[37] Viertl, R.: Statistical Methods for Fuzzy Data. John Wiley, Chichester 2011. | DOI | MR | Zbl

[38] Wang, J., Wu, Q.: Limiting behavior of the maximum of the partial sum for linearly negative quadrant dependent random variables under residual Ces` aro alpha-integrability assumption. J. Appl. Math. 2012 (2012), 1-10. | DOI | MR

[39] Wang, J. F., Zhang, L. X.: A Berry-Esseen theorem for weakly negatively dependent random variables and its applications. Acta Math. Hungar. 110 (2006), 4, 293-308. | DOI | MR | Zbl

[40] Wu, H. C.: The laws of large numbers for fuzzy random variables. Fuzzy Sets Systems 116 (2000), 245-262. | DOI | MR | Zbl

[41] Zhang, C. H.: Strong law of large numbers for sums of products. Ann. Probab. 24 (1996), 1589-1615. | DOI | MR | Zbl

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