• Journal of applied mathematics & informatics
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• 제32권1_2호
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• pp.55-60
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• 2014

In this paper, we will obtain Marcinkiewicz's type limit laws for fuzzy random sets as follows : Let {$X_n{\mid}n{\geq}1$} be a sequence of independent identically distributed fuzzy random sets and $E{\parallel}X_i{\parallel}^r_{{\rho_p}}$ < ${\infty}$ with $1{\leq}r{\leq}2$. Then the following are equivalent: $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ a.s. in the metric ${\rho}_p$ if and only if $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ in probability in the metric ${\rho}_p$ if and only if $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ in $L_1$ if and only if $S_n/n^{\frac{1}{r}}{\rightarrow}{\tilde{0}}$ in $L_r$ where $S_n={\Sigma}^n_{i=1}\;X_i$.

• Journal of applied mathematics & informatics
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• 제27권5_6호
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• pp.1459-1463
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• 2009

Recently, Zhao et.al [European Journal of Operational Research 169 (2006) 189-201] discussed a random fuzzy renewal process based on random fuzzy theory. They considered the rate of the random fuzzy renewal process and presented a random fuzzy elementary renewal theorem. They also established Blackwell's theorem in random fuzzy sense. But all these results are invalid. We give a counter example in this note.

• 한국통계학회:학술대회논문집
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• 한국통계학회 2003년도 추계 학술발표회 논문집
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• pp.183-188
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• 2003

In this paper, we establish some results on strong convergence for weighted sums of uniformly integrable fuzzy random variables taking values in the space of upper-semicontinuous fuzzy sets in R$^{p}$.

• Communications for Statistical Applications and Methods
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• 제9권3호
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• pp.871-876
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• 2002

In this paper, we establish some characterizations of tightness for a sequence of random elements taking values in the space of upper-semicontinuous fuzzy sets with compact support in R.

• 한국신뢰성학회:학술대회논문집
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• 한국신뢰성학회 2002년도 정기학술대회
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• pp.303-303
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• 2002

We obtain the necessary and sufficient condition of tightness for a sequence of random variables in the space of fuzzy sets with compact support in R.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 2003년도 춘계 학술대회 학술발표 논문집
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• pp.18-21
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• 2003

We propose some properties of fuzzy conditional expectation of hybrid number the addition of fuzzy number and random variable using Cartesian product distance for ${\alpha}$-level sets.

• Journal of the Korean Data and Information Science Society
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• 제17권1호
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• pp.195-204
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• 2006

In this paper, we consider a renewal process in which both the inter-arrival times and rewards are fuzzy random variables. We prove the uniform levelwise convergence of fuzzy renewal and fuzzy renewal rewards. These results improve the result of Popova and Wu[European J. Oper. Research 117(1999), 606-617] and the main result of Hwang [Fuzzy Sets and Systems 116 (2000), 237-244].

• 한국통계학회:학술대회논문집
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• 한국통계학회 2002년도 추계 학술발표회 논문집
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• pp.215-220
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• 2002

In this paper, we establish weak laws of large numbers for weighted sums of convex-compactly uniformly integrable fuzzy random variables taking values in the space of upper-semicontinuous fuzzy sets in R$^{p}$.

• Journal of applied mathematics & informatics
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• 제33권5_6호
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• pp.607-625
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• 2015

Recently, Wang et al. [Computers and Mathematics with Ap-plications 57 (2009) 1232-1248.] and Wang and Watada [Information Sci-ences 179 (2009) 4057-4069.] studied the renewal process and renewal reward process with fuzzy random inter-arrival times and rewards under the T-independence associated with any continuous Archimedean t-norm. But, their main results do not cover the classical theory of the random elementary renewal theorem and random renewal reward theorem when fuzzy random variables degenerate to random variables, and some given assumptions relate to the membership function of the fuzzy variable and the Archimedean t-norm of the results are restrictive. This paper improves the results of Wang and Watada and Wang et al. from a mathematical per-spective. We release some assumptions of the results of Wang and Watada and Wang et al. and completely generalize the classical stochastic renewal theorem and renewal rewards theorem.

• Korean Journal of Mathematics
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• 제2권
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• pp.57-64
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• 1994