• Communications for Statistical Applications and Methods
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• v.5 no.2
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• pp.439-445
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• 1998

In this paper we introduce the definition for fuzzy random set by Puri and Ralescu(1985) and show strong laws of large numbers for fuzzy random sets on Banach spaces.

• Korean Journal of Mathematics
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• v.16 no.4
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• pp.573-581
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• 2008

We obtain an improvement of strong laws of large numbers for independent fuzzy random variables.

• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.795-805
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• 2008

The aim of this paper is to extend the "classical degenerate convergence criterion" and the Feller weak law of large numbers to double adapted arrays of random variables.

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.7
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• pp.852-856
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• 2004

The present paper establishes a necessary and sufficient condition for weak convergence for weighted sums of compactly uniformly integrable level-continuous fuzzy random variables as a generalization of weak laws of large numbers for sums of fuzzy random variables.

• Proceedings of the Korean Statistical Society Conference
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• 2001.11a
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• pp.137-141
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• 2001

We can obtain SLLN's for fuzzy random variables with respect to the new metric $d_s$ on the space F(R) of fuzzy numbers in R. In this paper, we obtain a SLLN for convex tight random elements taking values in F(R).

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.10a
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• pp.9-15
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• 1998

In this paper, we introduce new results of law large numbers for mutually T-related fuzzy numbers, when T is Archimedean t-norm and spreads are random variables, and generalize earlier result of Fullr[FSS 45(1992) 299-303].

• Transactions of the Korean Society of Machine Tool Engineers
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• v.18 no.2
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• pp.187-193
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• 2009

Dynamic response of an elastic pendulum system under random excitations was studied by using the Lagrangian equations of motion which uses the kinetic and potential energy of a target system. The responses of random excitations were calculated by using Monte Carl simulation which uses the series of random numbers. The procedure of Monte Carlo simulation is generation of random numbers, system model, system output, and statistical management of output. When the levels of random excitations were changed, the expected responses of the pendulum system showed various responses.

• The Journal of the Korea Contents Association
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• v.6 no.5
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• pp.29-34
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• 2006

For the almost certainly convergent series $S_n=\sum_{i=1}^nV-i$ of independent random elements in Banach spaces, by investigating tail series laws of large numbers, the rate of convergence of the series $S_n$ to a random variable s is studied in this paper. More specifically, by studying the duality between the limiting behavior of the tail series $T_n=S-S_{n-1}=\sum_{i=n}^{\infty}V-i$ of random variables and that of Banach space valued random elements, an alternative way of proving a result of the previous work, which establishes the equivalence between the tail series weak law of large numbers and a limit law, is provided in a Banach space setting.

• International Journal of Computer Science & Network Security
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• v.24 no.4
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• pp.77-86
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• 2024

Using random numbers to represent uncertainty and unpredictability is essential in many industries. This is crucial in disciplines like computer science, cryptography, and statistics where the use of randomness helps to guarantee the security and dependability of systems and procedures. In computer science, random number generation is used to generate passwords, keys, and other security tokens as well as to add randomness to algorithms and simulations. According to recent research, the hardware random number generators used in billions of Internet of Things devices do not produce enough entropy. This article describes how raw data gathered by IoT system sensors can be used to generate random numbers for cryptography systems and also examines the results of these random numbers. The results obtained have been validated by successfully passing the FIPS 140-1 and NIST 800-22 test suites.

• Honam Mathematical Journal
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• v.33 no.4
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• pp.591-602
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• 2011

In this paper we establish the central limit theorem and the strong law of large numbers for linear random fields generated by identically distributed linear negative quadrant dependent random variables on $\mathbb{Z}^2$.