• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.513-520
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• 2005

We calculate the normal fuzzy probability for trigonometric fuzzy numbers defined by trigonometric functions. And we study the normal probability for some operations of two trigonometric fuzzy numbers. Furthermore, we calculate the normal fuzzy probability for some fuzzy numbers generated by operations.

• Communications of the Korean Mathematical Society
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• v.37 no.3
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• pp.765-800
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• 2022

Quantization for probability distributions concerns the best approximation of a d-dimensional probability distribution P by a discrete probability with a given number n of supporting points. In this paper, we have considered a probability measure generated by an infinite iterated function system associated with a probability vector on ℝ. For such a probability measure P, an induction formula to determine the optimal sets of n-means and the nth quantization error for every natural number n is given. In addition, using the induction formula we give some results and observations about the optimal sets of n-means for all n ≥ 2.

• Communications of the Korean Mathematical Society
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• v.21 no.2
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• pp.385-395
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• 2006

We study the exponential fuzzy probability for quadratic fuzzy number and trigonometric fuzzy number defined by quadratic function and trigonometric function, respectively. And we calculate the exponential fuzzy probabilities for fuzzy numbers driven by operations.

• Journal of information and communication convergence engineering
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• v.8 no.6
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• pp.677-681
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• 2010

This paper proposes a transmission probability control scheme for enhancing the performances of FSA-based RFID system. In order to maximize the system performance, the number of tags attempting to transmit their identifiers in a frame should be kept at a proper level. The reader calculates the transmission probability according to the number of tags within the identification range of reader and then broadcasts it to tags. Tags, in which their slot counter values reach to zero, attempt to transmit their identifiers with the received probability. Simulation results show that the proposed scheme can offer better throughput and delay performance than the conventional one regardless of the number of tags.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.8 no.2
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• pp.116-120
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• 2008

Clustering is a method for unsupervised learning. General clustering tools have been depended on statistical methods and machine learning algorithms. One of the popular clustering algorithms based on machine learning is the self organizing map(SOM). SOM is a neural networks model for clustering. SOM and extended SOM have been used in diverse classification and clustering fields such as data mining. But, SOM has had a problem determining optimal number of clusters. In this paper, we propose an improvement of SOM using gap statistic and probability distribution. The gap statistic was introduced to estimate the number of clusters in a dataset. We use gap statistic for settling the problem of SOM. Also, in our research, weights of feature nodes are updated by probability distribution. After complete updating according to prior and posterior distributions, the weights of SOM have probability distributions for optima clustering. To verify improved performance of our work, we make experiments compared with other learning algorithms using simulation data sets.

• Journal of the Korean Society of Safety
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• v.32 no.6
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• pp.1-8
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• 2017

P-PIE is a program developed to estimate failure probability of pipes and pressure vessels considering fatigue and stress corrosion crack growth. Using the program, crack growth simulation was performed with an initially existing crack in order to examine the effects of initial crack depth distribution on the leak probability of pipes. In the simulation stress corrosion crack growth was considered and several crack depth distribution models were used. From the results it was found that the initial crack depth distribution gives great effect on the leak probability of pipes. The log-normal distribution proposed by Khaleel and Simonen gives lower leak probability compared other exponential distribution models. The effects of the number and the quality of pre-service and in-service inspections on the leak probability were also examined and it was recognized that the number and the quality of pre-service and in-service inspections are also give great effect on the leak probability. In order to reduce the leak probability of pipes in plants it is very important to improve the quality of inspections. When in-service inspection is performed every 10 years and the quality of inspection is above the very good level, the leak probability shows nearly constant value after the first inspection for an initially existing crack.

• Communications of the Korean Mathematical Society
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• v.38 no.2
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• pp.431-450
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• 2023

The basic goal of quantization for probability distribution is to reduce the number of values, which is typically uncountable, describing a probability distribution to some finite set and thus to make an approximation of a continuous probability distribution by a discrete distribution. It has broad application in signal processing and data compression. In this paper, first we define the uniform distributions on different curves such as a line segment, a circle, and the boundary of an equilateral triangle. Then, we give the exact formulas to determine the optimal sets of n-means and the nth quantization errors for different values of n with respect to the uniform distributions defined on the curves. In each case, we further calculate the quantization dimension and show that it is equal to the dimension of the object; and the quantization coefficient exists as a finite positive number. This supports the well-known result of Bucklew and Wise [2], which says that for a Borel probability measure P with non-vanishing absolutely continuous part the quantization coefficient exists as a finite positive number.

• School Mathematics
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• v.17 no.2
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• pp.241-255
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• 2015

The purpose of this study is to analyze teachers' understanding on generating random number in Monte Carlo simulation and to provide educational implications in school practice. The results showed that the 70% of the teachers selected wrong ideas from three types for random-number as strategies for problem solving a probability problem and also they make some errors to justify their opinion. The first kind of the errors was that the probability of a point or boundary was equal to the value of the probability density function in the continuous probability distribution. The second kind of the errors was that the teachers failed to recognize that the sample space has been changed by conditional probability. The third kind of the errors was that when two random variables X, Y are independence of each other, then only, joint probability distribution is satisfied $P(X=x,\;Y=y)=p(X=x){\times}P(Y=y{\mid}X=x)$.

• International Journal of Highway Engineering
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• v.15 no.5
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• pp.157-166
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• 2013

PURPOSES : This study is to analyze expected effect of a accident decrease when motorcycle safety inspection is introduced. METHODS : Based on the literature review of effect of 4-wheel vehicle inspection, probability of occurring accidents among defective motorcycles are calculated by using the number of estimated defective motorcycles and accidents resulting from defects of motorcycles. Then, the number of decreased accidents which is resulting from eliminating defects of motorcycles by safety inspection is estimated by using probability of occurring accidents among defective motorcycles. RESULTS : If the ratio of eliminating defects of motorcycles is 95% after motorcycle safety inspection, the effects of accident decrease of motorcycle safety inspection are analyzed from 2005 to 2008. As a result, 46,292 defective motorcycles are repaired and 1,376 accidents are prevented when the probability of occurring accidents among defective motorcycles is 2.97%. CONCLUSIONS : This study suggests the expected effect of motorcycle safety inspection is that the inspection can prevent 1,376 motorcycle accidents. However, the number of preventing motorcycle accidents are small, compared with the total number of motorcycle accidents because there are limitations to investigate the causes of defective motorcycle accidents. A more precise analysis of the expected effect of motorcycle inspection is possible when a systematic investigation of the causes of the accidents is implemented.

• Journal of Korean Institute of Industrial Engineers
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• v.11 no.2
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• pp.19-27
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• 1985

Optimal numbers of repeat inspections are obtained for a single inspector who has a fixed probability of detecting a nonconforming item on each inspection and will continue to inspect until further inspection is not warranted when comparing the expected increase of total gain with the inspection cost. It is assumed that the detection probability decreases as the number of repeat inspections increases, and that the lot to be inspected contains an unknown but Poisson distributed number of nonconforming items.