• Journal of applied mathematics & informatics
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• v.37 no.1_2
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• pp.65-71
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• 2019

In this paper we give some properties related to fuzzy functions on complete residuated lattices.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.62 no.4
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• pp.544-553
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• 2013

In this paper, we propose the pattern classifier of Radial Basis Function Neural Networks(RBFNNs) for diagnosis of 3-phase partial discharge. Conventional methods map the partial discharge/noise data on 3-PARD map, and decide whether the partial discharge occurs or not from 3-phase or neutral point. However, it is decided based on his own subjective knowledge of skilled experter. In order to solve these problems, the mapping of data as well as the classification of phases are considered by using the general 3-PARD map and PA method, and the identification of phases occurring partial discharge/noise discharge is done. In the sequel, the type of partial discharge occurring on arbitrary random phase is classified and identified by fuzzy clustering-based polynomial Radial Basis Function Neural Networks(RBFNN) classifier. And by identifying the learning rate, momentum coefficient, and fuzzification coefficient of FCM fuzzy clustering with the aid of PSO algorithm, the RBFNN classifier is optimized. The virtual simulated data and the experimental data acquired from practical field are used for performance estimation of 3-phase partial discharge pattern classifier.

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.4.2-4
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• 2003

In this paper, we describe how to approximate the solutions of partial differential equations by bicubic spline functions whose interpolation errors at non-grid points are smaller in general than those by linear interpolations of the original solution at grid points. We show that the bicubic spline function can be represented exactly or approximately by a fuzzy system, and that the resulting fuzzy rule table shows the contours of the solution function. Thus, the fuzzy rule table is identified as a digital image and the contours in the rule table provide approximate contours of the solution of partial differential equations. Several illustrative examples are included.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.8
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• pp.1615-1623
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• 2009

In order to develop reliable on-site partial discharge (PD) pattern recognition algorithm, we introduce Type-2 Fuzzy Neural Networks (T2FNNs) optimized by means of Particle Swarm Optimization(PSO). T2FNNs exploit Type-2 fuzzy sets which have a characteristic of robustness in the diverse area of intelligence systems. Considering the on-site situation where it is not easy to obtain voltage phases to be used for PRPDA (Phase Resolved Partial Discharge Analysis), the PD data sets measured in the laboratory were artificially changed into data sets with shifted voltage phases and added noise in order to test the proposed algorithm. Also, the results obtained by the proposed algorithm were compared with that of conventional Neural Networks(NNs) as well as the existing Radial Basis Function Neural Networks (RBFNNs). The T2FNNs proposed in this study were appeared to have better performance when compared to conventional NNs and RBFNNs.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.3 no.1
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• pp.13-17
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• 2003

A continuous solution of the Dirichlet boundary value problem for the heat equation $u_t$＝$a2u_{xx}$ using a fuzzy system is described. We first apply the Crank-Nicolson method to obtain a discrete solution at the grid points for the heat equation. Then we find a continuous function to represent approximately the discrete values at the grid points in the form of a bicubic spline function (equation omitted) that can in turn be represented exactly by a fuzzy system. We show that the computed values at non-grid points using the bicubic spline function is much smaller than the ones obtained by linear interpolations of the values at the grid points. We also show that the fuzzy rule table in the fuzzy system representation of the bicubic spline function can be viewed as a gray scale image. Hence, the fuzzy rules provide a visual representation of the functions of two variables where the contours of different levels for the function are shown in different gray scale levels

• The Transactions of The Korean Institute of Electrical Engineers
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• v.66 no.9
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• pp.1392-1401
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• 2017

In this study, the design methodology of pattern classification is introduced for avoiding faults through partial discharge occurring in the power facilities and local sites. In order to classify some partial discharge types according to the characteristics of each feature, the model is constructed by using the Radial Basis Function Neural Networks(RBFNNs) and Particle Swarm Optimization(PSO). In the input layer of the RBFNNs, the feature vector is searched and the dimension is reduced through Principal Component Analysis(PCA) and PSO. In the hidden layer, the fuzzy coefficients of the fuzzy clustering method(FCM) are tuned using PSO. Raw datasets for partial discharge are obtained through the Motor Insulation Monitoring System(MIMS) instrument using an Epoxy Mica Coupling(EMC) sensor. The preprocessed datasets for partial discharge are acquired through the Phase Resolved Partial Discharge Analysis(PRPDA) preprocessing algorithm to obtain partial discharge types such as void, corona, surface, and slot discharges. Also, when the amplitude size is considered as two types of both the maximum value and the average value in the process for extracting the preprocessed datasets, two different kinds of feature datasets are produced. In this study, the classification ratio between the proposed RBFNNs model and other classifiers is shown by using the two different kinds of feature datasets, and also we demonstrate the proposed model shows superiority from the viewpoint of classification performance.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.3
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• pp.216-220
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• 2007

Camera calibration in machine vision is the process of determining the intrinsic camera parameters and the three-dimensional (3D) position and orientation of the camera frame relative to a certain world coordinate system. On the other hand, Takagi-Sugeno-Kang (TSK) fuzzy system is a very popular fuzzy system and approximates any nonlinear function to arbitrary accuracy with only a small number of fuzzy rules. It demonstrates not only nonlinear behavior but also transparent structure. In this paper, we present a novel and simple technique for camera calibration for machine vision using TSK fuzzy model. The proposed method divides the world into some regions according to camera view and uses the clustered 3D geometric knowledge. TSK fuzzy system is employed to estimate the camera parameters by combining partial information into complete 3D information. The experiments are performed to verify the proposed camera calibration.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.13 no.4
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• pp.254-268
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• 2013

For real-world clustering tasks, the input data is typically not easily separable due to the highly complex data structure or when clusters vary in size, density and shape. Kernel-based clustering has proven to be an effective approach to partition such data. In this paper, we provide an overview of several fuzzy kernel clustering algorithms. We focus on methods that optimize an fuzzy C-mean-type objective function. We highlight the advantages and disadvantages of each method. In addition to the completely unsupervised algorithms, we also provide an overview of some semi-supervised fuzzy kernel clustering algorithms. These algorithms use partial supervision information to guide the optimization process and avoid local minima. We also provide an overview of the different approaches that have been used to extend kernel clustering to handle very large data sets.

• The Transactions of the Korean Institute of Electrical Engineers D
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• v.50 no.9
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• pp.430-438
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• 2001

In this study, we introduce the adaptive Polynomial Neuro-Fuzzy Networks(PNFN) architecture generated from the fusion of fuzzy inference system and PNN algorithm. The PNFN dwells on the ideas of fuzzy rule-based computing and neural networks. Fuzzy inference system is applied in the 1st layer of PNFN and PNN algorithm is employed in the 2nd layer or higher. From these the multilayer structure of the PNFN is constructed. In order words, in the Fuzzy Inference System(FIS) used in the nodes of the 1st layer of PNFN, either the simplified or regression polynomial inference method is utilized. And as the premise part of the rules, both triangular and Gaussian like membership function are studied. In the 2nd layer or higher, PNN based on GMDH and regression polynomial is generated in a dynamic way, unlike in the case of the popular multilayer perceptron structure. That is, the PNN is an analytic technique for identifying nonlinear relationships between system's inputs and outputs and is a flexible network structure constructed through the successive generation of layers from nodes represented in partial descriptions of I/O relatio of data. The experiment part of the study involves representative time series such as Box-Jenkins gas furnace data used across various neurofuzzy systems and a comparative analysis is included as well.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2006.05a
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• pp.56-58
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• 2006

Camera calibration in machine vision is the process of determining the intrinsic cameara parameters and the three-dimensional (3D) position and orientation of the camera frame relative to a certain world coordinate system. On the other hand, Takagi-Sugeno-Kang (TSK) fuzzy system is a very popular fuzzy system and approximates any nonlinear function to arbitrary accuracy with only a small number of fuzzy rules. It demonstrates not only nonlinear behavior but also transparent structure. In this paper, we present a novel and simple technique for camera calibration for machine vision using TSK fuzzy model. The proposed method divides the world into some regions according to camera view and uses the clustered 3D geometric knowledge. TSK fuzzy system is employed to estimate the camera parameters by combining partial information into complete 3D information. The experiments are performed to verify the proposed camera calibration.