Strong laws of large numbers for t-norm-based addition of fuzzy set-valued random variables

2013 ◽  
Vol 223 ◽  
pp. 26-38 ◽  
Author(s):  
Dug Hun Hong
Keyword(s):  
Fuzzy Set ◽  
Random Variables ◽  
Laws Of Large Numbers ◽  
Strong Laws ◽  
Large Numbers

LAWS OF LARGE NUMBERS FOR WEIGHTED SUMS OF FUZZY SET-VALUED RANDOM VARIABLES

2004 ◽  
Vol 12 (06) ◽  
pp. 811-825 ◽  
Author(s):  
LI GUAN ◽  
SHOUMEI LI
Keyword(s):  
Fuzzy Set ◽  
Hausdorff Metric ◽  
Random Variables ◽  
Random Variable ◽  
Weighted Sums ◽  
Laws Of Large Numbers ◽  
Strong Laws ◽  
Large Numbers

In this paper, we shall present weak and strong laws of large numbers (WLLN's and SLLN's) for weighted sums of independent (not necessarily identically distributed) fuzzy set-valued random variables in the sense of the extended Hausdorff metric [Formula: see text], based on the result of set-valued random variable obtained by Taylor and Inoue32,33. This work is a continuation of Li and Ogura20.

scholarly journals On Chung-Teicher type strong law for arrays of vector-valued random variables

2004 ◽  
Vol 2004 (9) ◽  
pp. 443-458
Author(s):  
Anna Kuczmaszewska
Keyword(s):  
Banach Space ◽  
Random Variables ◽  
Strong Law ◽  
Laws Of Large Numbers ◽  
Strong Laws ◽  
Large Numbers ◽  
Random Elements ◽  
Vector Valued

We study the equivalence between the weak and strong laws of large numbers for arrays of row-wise independent random elements with values in a Banach spaceℬ. The conditions under which this equivalence holds are of the Chung or Chung-Teicher types. These conditions are expressed in terms of convergence of specific series ando(1)requirements on specific weighted row-wise sums. Moreover, there are not any conditions assumed on the geometry of the underlying Banach space.

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