• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.1169-1183
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• 2008

In this paper, a method to find the weighted possibilistic variance and moments about the mean value of fuzzy numbers via applying a difuzzification using minimizer of the weighted distance between two fuzzy numbers is introduced. In this way, we obtain the nearest weighted point with respect to a fuzzy number, this main result is a new and interesting alternative justification to define of weighted mean of a fuzzy number. Considering this point and the weighted distance quantity, we introduce the weighted possibilistic mean (WPM) value and the weighted possibilistic variance(WPV) of fuzzy numbers. This paper shows that WPM is the nearest weighted point to fuzzy number and the WPV of fuzzy number is preserved more properties of variance in probability theory so that it can simply introduce the possibilistic moments about the mean of fuzzy numbers without problem. The moments of fuzzy numbers play an important role to estimate of parameters, skewness, kurtosis in many of fuzzy times series models.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.34S no.3
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• pp.97-107
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• 1997

Image segmentation is teh important step in image infromation extraction for computer vison sytems. Fuzzy clustering methods have been used extensively in color image segmentation. Most analytic fuzzy clustering approaches are derived from the fuzzy c-means (FCM) algorithm. The FCM algorithm uses th eprobabilistic constraint that the memberships of a data point across classes sum to 1. However, the memberships resulting from the FCM do not always correspond to the intuitive concept of degree of belongingor compatibility. moreover, the FCM algorithm has considerable trouble above under noisy environments in the feature space. Recently, the possibilistic C-mean (PCM) for solving growing for color image segmentation. In the PCM, the membersip values may be interpreted as degrees of possibility of the data points belonging to the classes. So, the problems in the FCM can be solved by the PCM. The clustering results by just PCM are not smoothly bounded, and they often have holes. So, the region growing was used as a postprocessing. In our experiments, we illustrated that the proposed method is reasonable than the FCM in noisy enviironments.

• Journal of the Korea Society of Computer and Information
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• v.15 no.1
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• pp.43-50
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• 2010

Fuzzy c-means (FCM) and possibilistic c-means (PCM) are the two most well-known clustering algorithms in fuzzy clustering area, and have been applied in many applications in their original or modified forms. However, FCM's noise sensitivity problem and PCM's overlapping cluster problem are also well known. Recently there have been several attempts to combine both of them to mitigate the problems and possibilistic fuzzy c-means (PFCM) showed promising results. In this paper, we proposed a modified PFCM using regularization to reduce noise sensitivity in PFCM further. Regularization is a well-known technique to make a solution space smooth and an algorithm noise insensitive. The proposed algorithm, PFCM with regularization (PFCM-R), can take advantage of regularization and further reduce the effect of noise. Experimental results are given and show that the proposed method is better than the existing methods in noisy conditions.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2007.11a
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• pp.423-426
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• 2007

클러스터링은 주어진 데이터 포인트들을 주어진 개수의 그룹으로 나누는 비지도 학습의 한 방법이다. 클러스터링의 방법 중 하나로 널리 알려진 퍼지 클러스터링은 하나의 포인트가 모든 클러스터에 서로 다른 정도로 소속될 수 있도록 함으로써 각 포인트가 하나의 클러스터에만 속할 수 있도록 하는 K-means와 같은 방법에 비해 자연스러운 클러스터 형태의 유추가 가능하고, 잡음에 강한 장점이 있다. 이 논문에서는 기존의 퍼지 클러스터링 방법 중 소속도(membership)와 전형성(typicality)을 동시에 계산해 낼 수 있는 Possibilistic Fuzzy C-Means (PFCM) 방법에 Gath-Geva (GG)의 방법 을 적용하여 PFCM을 확장한다. 제안한 방법은 PFCM의 장점을 그대로 가지면서도, GG의 거리 척도에 의해 클러스터들 사이의 경계를 강조함으로써 분류 목적에 적합한 소속도를 계산할 수 있으며, 전형성은 가우스 형태의 분포에서 생성된 포인트들의 분포 함수를 정확하게 모사함으로써 확률 밀도 추정의 방법으로도 사용될 수 있다. 또한 GG 방법은 Gustafson-Kessel 방법과 달리 클러스터에 포함된 포인트의 개수가 확연히 차이 나는 경우에도 정확한 결과를 얻을 수 있다는 사실을 실험 결과를 통해 확인할 수 있었다.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.24 no.9B
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• pp.1731-1741
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• 1999

Color images are often corrupted by the noise due to noisy sensors or channel transmission errors. Some filters such as vector media and vector $\alpha$-trimmed mean filter have bee used for color noise removal. In this paper, We propose the fuzzy cluster filters based on the possibilistic c-means clustering, because the possibilistic c-means clustering can get robust memberships in noisy environments. Also, we propose weighted vector $\alpha$-trimmed mean filter to improve the conventional vector $\alpha$-trimmed mean filter. In this filter, the central data are more weighted than the outlying data. In this paper, we implemented the color noise generator to evaluate the performance of the proposed filters in the color noise environments. The NCD measure and visual measure by human observer are used for evaluation the performance of the proposed filters. In the experiment, proposed fuzzy cluster filters in the sense of NCD measure gave the best performance over conventional filters in the mixed noise. Simulation results showed that proposed weighted vector $\alpha$-trimmed mean filters better than the conventional vector $\alpha$-trimmed mean filter in any kinds of noise.

• Proceedings of the Korea Society for Industrial Systems Conference
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• 1999.12a
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• pp.315-323
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• 1999

The measuring systems of auto-parts are most of greater part very expensive. This paper tries to study to make a low-cost measuring equipment. There's several kinds of parts in automobile. In this study, we take aircon-switch called magnet coil-housing as the object of measurements. The measurements of this product is currently in difficult situations at factory. In the case of the mesuring objects being big sizes and camera sensor having under 410000 pixels, the key point is the number of pixels not to be changed whenever the same object is measured under the same position. We modified and used fuzzy c-means algorithm to get mostly without the change of the numbers of pixels exactly. Also, the standardized ruler is necessary to measure the length of the object but it is not easy to get the precised ruler. Therefore, the standard length has been taken as the mean value of the pixels in the previous passed objects manually obtained at factory. The results are displayed on monitor and transferred these signals to the microprocessor through RSC-232 port to determine a good or bad of products.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.13 no.1
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• pp.177-185
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• 2009

Cluster analysis or clustering is a kind of unsupervised learning method in which a set of data points is divided into a given number of homogeneous groups. Fuzzy clustering method, one of the most popular clustering method, allows a point to belong to all the clusters with different degrees, so produces more intuitive and natural clusters than hard clustering method does. Even more some of fuzzy clustering variants have noise-immunity. In this paper, we improved the Possibilistic Fuzzy C-Means (PFCM), which generates a membership matrix as well as a typicality matrix, using Gath-Geva (GG) method. The proposed method has a focus on the boundaries of clusters, which is different from most of the other methods having a focus on the centers of clusters. The generated membership values are suitable for the classification-type applications. As the typicality values generated from the algorithm have a similar distribution with the values of density function of Gaussian distribution, it is useful for Gaussian-type density estimation. Even more GG method can handle the clusters having different numbers of data points, which the other well-known method by Gustafson and Kessel can not. All of these points are obvious in the experimental results.

• Journal of applied mathematics & informatics
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• v.42 no.4
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• pp.831-854
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• 2024

The transportation problem (TP) is one of the earliest and the most significant implementations of linear programming problem (LPP). It is a specific type of LPP that mostly works with logistics and it is connected to day-to-day activities in our everyday lives. Nowadays decision makers (DM's) aim to reduce the transporting expenses and simultaneously aim to reduce the transporting time of the distribution system so the bi-objective transportation problem (BOTP) is established in the research. In real life, the transportation parameters are naturally uncertain due to insufficient data, poor judgement and circumstances in the environment, etc. In view of this, neutrosophic bi-objective transportation problem (NBOTP) is introduced in this paper. By introducing single-valued trapezoidal neutrosophic numbers (SVTrNNs) to the co-efficient of the objective function, supply and demand constraints, the problem is formulated. The DM's aim is to determine the optimal compromise solution for NBOTP. The extended weighted possibility mean for single-valued trapezoidal neutrosophic numbers based on [40] is proposed to transform the single-valued trapezoidal neutrosophic BOTP (SVTrNBOTP) into its deterministic BOTP. The transformed deterministic BOTP is then solved using the dripping method [10]. Numerical examples are provided to illustrate the applicability, effectiveness and usefulness of the solution approach. A sensitivity analysis (SA) determines the sensitivity ranges for the objective functions of deterministic BOTP. Finally, the obtained optimal compromise solution from the proposed approach provides a better result as compared to the existing approaches and conclusions are discussed for future research.

• Journal of Korea Society of Industrial Information Systems
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• v.4 no.4
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• pp.7-14
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• 1999

The measuring systems of auto-parts are most of greater part very expensive. This paper tries to study to make a low-cost measuring equipment there's several kinds of parts in automobile. In this study, we take aircon-switch called magnet coil-housing as the object of measurements. The measurements of this product is currently in difficult situations at factory. In the case of the mesuring objects being big sizes and camera sensor having under 410000 pixels, the key point is the number of pixels not to be changed whenever the same object is measured under the same position. We modified and used fuzzy c-means algorithm to get mostly without the change of the numbers of pixels exactly. Also, the standardized ruler is necessary to measure the length of the object but it is not easy to get the precised ruler. Therefore, the standard length has been taken as the mean value of the pixels in the previous passed objects manually obtained at factory. The results are displayed on monitor and transferred these signals to the microprocessor through RSC-232 port to determine a good or bad of products.