• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.9 no.3
• /
• pp.219-223
• /
• 2009

Recently, Zhao et al. [Fuzzy Optimization and Decision Making (2007) 6, 279-295] characterized the interarrival times as fuzzy random variables and presented a fuzzy random elementary renewal theorem on the limit value of the expected renewal rate of the process in the fuzzy random renewal process. They also depicted both the interarrival times and rewards are depicted as fuzzy random variables and provided fuzzy random renewal reward theorem on the limit value of the long run expected reward per unit time in the fuzzy random renewal reward process. In this note, we simplify the proofs of two main results of the paper.

• Journal of applied mathematics & informatics
• /
• v.27 no.5_6
• /
• pp.1459-1463
• /
• 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.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 1998.06a
• /
• pp.696-700
• /
• 1998

Fuzzy random variables with piecewise linear membership functions are introduced from a practical viewpoint. The estimation of the expected values of these fuzzy random variables is also discussed and statistical application is denonstratied by using a real data set.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2004.04a
• /
• pp.394-397
• /
• 2004

In this paper, we consider interval number-valued random variables and fuzzy number-valued random variables and discuss Choquet integrals of them. Using these properties, we define the Choquet expected value of fuzzy number-valued random variables which is a natural generalization of the Lebesgue expected value of Lebesgue expected value of fuzzy random variables. Furthermore, we discuss some application of them.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2003.05a
• /
• pp.18-21
• /
• 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
• /
• v.14 no.1
• /
• pp.75-82
• /
• 2003

In this paper, a general convergence theorem of fuzzy random variables is considered. Using this result, we can easily prove the recent result of Joo et al. (2001) and generalize the recent result of Kim(2000).

• Journal of the Korean Data and Information Science Society
• /
• v.9 no.2
• /
• pp.113-118
• /
• 1998

In this paper we study central limit theorem(C.L.T.) and law of iterated logarithm (L.I.L.) for fuzzy random variables with respect to Hausdorff distance.

• Nonlinear Functional Analysis and Applications
• /
• v.27 no.3
• /
• pp.621-640
• /
• 2022

The aim of this study is to establish some mean convergence theorems for double array of fuzzy random variables in metric space endowed with a convex combination operation under various assumptions.

• Journal of applied mathematics & informatics
• /
• v.33 no.5_6
• /
• pp.607-625
• /
• 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.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.15 no.1
• /
• pp.98-103
• /
• 2005

In this paper, we consider interval number-valued random variables and fuzzy number-valued random variables and discuss Choquet integrals of them. Using these properties, we define the Choquet expected value of fuzzy number-valued random variables which is a natural generalization of the Lebesgue expected value of fuzzy random variables. Furthermore, we discuss some application of them.