• International Journal of Fuzzy Logic and Intelligent Systems
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• 제13권3호
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• pp.215-223
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• 2013

In this paper, we present some results on weak laws of large numbers for weighted sums of fuzzy random variables taking values in the space of normal and upper-semicontinuous fuzzy sets with compact support in a separable real Banach space. First, we give weak laws of large numbers for weighted sums of strong-compactly uniformly integrable fuzzy random variables. Then, we consider the case that the weighted averages of expectations of fuzzy random variables converge. Finally, weak laws of large numbers for weighted sums of strongly tight or identically distributed fuzzy random variables are obtained as corollaries.

• 대한수학회지
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• 제57권2호
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• pp.359-381
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• 2020

In this paper we established new results of existence of conditional expectation for closed convex and unbounded Pettis integrable random sets without assuming the Radon Nikodym property of the Banach space. As application, new versions of multivalued Lévy's martingale convergence theorem are proved by using the Slice and the linear topologies.

• 한국지능시스템학회:학술대회논문집
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• 한국지능시스템학회 2008년도 춘계학술대회 학술발표회 논문집
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• pp.131-132
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• 2008

In this paper, we consider interval probability as a unifying concept for uncertainty and Choquet integrals with resect to a capacity functional. By using interval probability, we will define an interval-valued capacity functional and Choquet integrals with respect to an interval-valued capacity functional. Furthermore, we investigate Choquet Choquet weak convergence of interval-valued capacity functionals of random sets.

• 대한수학회지
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• 제55권4호
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• pp.833-848
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• 2018

In this paper we study the existence of conditional expectation for closed and convex valued Pettis-integrable random sets without assuming the Radon Nikodym property of the Banach space. New version of multivalued dominated convergence theorem of conditional expectation and multivalued $L{\acute{e}}vy^{\prime}s$ martingale convergence theorem for integrable and Pettis integrable random sets are proved.

• 대한수학회지
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• 제51권5호
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• pp.1075-1088
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• 2014

We consider random fractal sets with random recursive constructions in which the contracting vectors have different distributions at different stages. We prove that the random fractal associated with such construction has a constant packing dimension almost surely and give an explicit formula to determine it.

• Korean Journal of Mathematics
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• 제21권4호
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• pp.383-399
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• 2013

In this paper, we establish two types of strong law of large numbers for fuzzy random variables taking values on the space of normal and upper-semicontinuous fuzzy sets with compact support in a separable Banach space. The first result is SLLN for strong-compactly uniformly integrable fuzzy random variables, and the other is the case of that the averages of its expectations converges.

• Structural Engineering and Mechanics
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• 제60권6호
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• pp.953-977
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• 2016

Modern performance-based design methods require ways to determine the factual behavior of structures subjected to earthquakes. Drift ratio demands are important measures of structural and/or nonstructural damage of the structures in performance-based design. In this study, global drift ratio and interstory drift ratio demands, obtained by nonlinear time history analysis of three generic RC frames using code-compatible ground motion record sets, are statistically evaluated. Several ground motion record sets compatible with elastic design spectra defined for the local soil classes in Turkish Earthquake Code are used for the analyses. Variation of the drift ratio demands obtained from ground motion records in the sets and difference between the mean of drift ratio demands calculated for ground motion sets are evaluated. The results of the study indicate that i) variation of maximum drift ratio demands in the sets were high; ii) different drift ratio demands are calculated using different ground motion record sets although they are compatible with the same design spectra; iii) the effect of variability due to random causes on the total variability of drift ratio demands is much larger than the effect of variability due to differences between the mean of ground motion record sets; iv) global and interstory drift ratio demands obtained for different ground motion record sets can be accepted as simply random samples of the same population at %95 confidence level. The results are valid for all the generic frames and local soil classes considered in this study.

• 대한원격탐사학회지
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• 제22권3호
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• pp.211-219
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• 2006

A random forests classifier is applied to multi-sensor data fusion for supervised land-cover classification in order to account for the importance of variable. The random forests approach is a non-parametric ensemble classifier based on CART-like trees. The distinguished feature is that the importance of variable can be estimated by randomly permuting the variable of interest in all the out-of-bag samples for each classifier. Two different multi-sensor data sets for supervised classification were used to illustrate the applicability of random forests: one with optical and polarimetric SAR data and the other with multi-temporal Radarsat-l and ENVISAT ASAR data sets. From the experimental results, the random forests approach could extract important variables or bands for land-cover discrimination and showed reasonably good performance in terms of classification accuracy.

• 한국지능시스템학회논문지
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• 제18권6호
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• pp.837-841
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• 2008

In this paper, we consider interval probability as a unifying concept for uncertainty and Choquet integrals with resect to a capacity functional. By using interval probability, we will define an interval-valued capacity functional and Choquet integral with respect to an interval-valued capacity functional. Furthermore, we investigate Choquet weak convergence of interval-valued capacity functionals of random sets.

• 대한수학회지
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• 제53권3호
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• pp.503-517
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• 2016

For positive integers d and n, let $[n]^d$ be the set of all vectors ($a_1,a_2,{\cdots},a_d$), where ai is an integer with $0{\leq}a_i{\leq}n-1$. A subset S of $[n]^d$ is called a Sidon set if all sums of two (not necessarily distinct) vectors in S are distinct. In this paper, we estimate two numbers related to the maximum size of Sidon sets in $[n]^d$. First, let $\mathcal{Z}_{n,d}$ be the number of all Sidon sets in $[n]^d$. We show that ${\log}(\mathcal{Z}_{n,d})={\Theta}(n^{d/2})$, where the constants of ${\Theta}$ depend only on d. Next, we estimate the maximum size of Sidon sets contained in a random set $[n]^d_p$, where $[n]^d_p$ denotes a random set obtained from $[n]^d$ by choosing each element independently with probability p.