• Korean Journal of Mathematics
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• v.28 no.1
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• pp.75-87
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• 2020

Category F Rel of fuzzy sets and relations does not form a topos. J. Harding, C. Walker and E. Walker [3] showed that FRel has a tensor product and V. Durov [1] introduced basic definitions related to the notion of vectoid endowed with a tensor product. In this paper, we show that FRel forms a quasi topos. Also we show that there are quasi power objects in FRel. And by the use of the concepts of FRel and quasi topos, we get the logic operators of FRel. Moreover, we show that FRel forms a vectoid.

• Journal of the Korean Institute of Telematics and Electronics B
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• v.32B no.10
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• pp.1358-1363
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• 1995

This paper presents a new learning method for a noise tolerant Fuzzy ART. In the conventional Fuzzy ART, the top-down and bottom-up weight vectors have the same value. They are updated by a fuzzy AND operation between the input vector and the current value of the top-down or bottom- up weight vectors. However, it can not prevent the abrupt change of the weight vector and can not achieve good performance for a noisy input vector. To solve the problems, we updated using the weighted sum of the input vector and the current value of the top-down vector. To achieve stability, the bottom-up weight vector is updated using the fuzzy AND operation between the newly learned top-down vector and the current value of the bottom-up vector. Computer simulations show that the proposed method prominently resolves the category proliferation problem without increasing the training epoch for stabilization in noisy environments.

• Journal of the Korean Institute of Intelligent Systems
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• v.18 no.5
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• pp.638-641
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• 2008

In this paper, a model to classify the method using the fuzzy TAM with preprocessing of data was developed. The preprocessing method can be divide the problem using the characteristics in the case of category type factor. In case of continuous type factor, if there was exist factor's range which is not overlapping by class, the data belong to the range was fixed and eliminated in classification. After these preprocessing of data, classified operation of Fuzzy TAM is performed.

• Proceedings of the KIEE Conference
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• 2005.10b
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• pp.155-157
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• 2005

We propose a new category of hybrid multi-layer neural networks with hetero nodes such as Fuzzy Set based Polynomial Neurons (FSPNs) and Polynomial Neurons (PNs). These networks are based on a genetically optimized multi-layer perceptron. We develop a comprehensive design methodology involving mechanisms of genetic optimization and genetic algorithms, in particular. The augmented genetically optimized HFPNN (namely gHFPNN) results in a structurally optimized structure and comes with a higher level of flexibility in comparison to the one we encounter in the conventional HFPNN. The GA-based design procedure being applied at each layer of HFPNN leads to the selection of preferred nodes (FPNs or PNs) available within the HFPNN. In the sequel, two general optimization mechanisms are explored. First, the structural optimization is realized via GAs whereas the ensuing detailed parametric optimization is carried out in the setting of a standard least square method-based learning. The performance of the gHFPNNs quantified through experimentation where we use a number of modeling benchmarks-synthetic and experimental data already experimented with in fuzzy or neurofuzzy modeling.

• Proceedings of the IEEK Conference
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• summer
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• pp.447-450
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• 2004

This paper proposes remotely sensed image classification method by fuzzy c-means clustering algorithm using average intra-cluster distance. The average intra-cluster distance acquires an average of the vector set belong to each cluster and proportionates to its size and density. We perform classification according to pixel's membership grade by cluster center of fuzzy c-means clustering using the mean-values of training data about each class. Fuzzy c-means algorithm considered membership degree for inter-cluster of each class. And then, we validate degree of overlap between clusters. A pixel which has a high degree of overlap applies to the maximum likelihood classification method. Finally, we decide category by comparing with fuzzy membership degree and likelihood rate. The proposed method is applied to IKONOS remote sensing satellite image for the verifying test.

• KIEE International Transaction on Systems and Control
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• v.12D no.1
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• pp.12-17
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• 2002

We propose a new category of neurofuzzy networks- Self-organizing Neural Networks(SONN) with fuzzy polynomial neurons(FPNs) and discuss a comprehensive design methodology supporting their development. Two kinds of SONN architectures, namely a basic SONN and a modified SONN architecture are dicussed. Each of them comes with two types such as the generic and the advanced type. SONN dwells on the ideas of fuzzy rule-based computing and neural networks. Simulation involves a series of synthetic as well as experimental data used across various neurofuzzy systems. A comparative analysis is included as well.

• Journal of Institute of Control, Robotics and Systems
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• v.7 no.8
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• pp.664-674
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• 2001

In this paper, as a new category of fuzzy-neural networks architecture, we propose Fuzzy Polynomial Neural Networks (FPNN) and discuss a comprehensive design methodology related to its architecture. FPNN dwells on the ideas of fuzzy rule-based computing and neural networks. The FPNN architecture consists of layers with activation nodes based on fuzzy inference rules. Here each activation node is presented as Fuzzy Polynomial Neuron(FPN). The conclusion part of the rules, especially the regression polynomial, uses several types of high-order polynomials such as linear, quadratic and modified quadratic. As the premise part of the rules, both triangular and Gaussian-like membership functions are studied. It is worth stressing that the number of the layers and the nods in each layer of the FPNN are not predetermined, unlike in the case of the popular multilayer perceptron structure, but these are generated in a dynamic manner. With the aid of two representative time series process data, a detailed design procedure is discussed, and the stability is introduced as a measure of stability of the model for the comparative analysis of various architectures.

• Proceedings of the Korea Society for Energy Engineering kosee Conference
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• 1999.11a
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• pp.119-124
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• 1999

A selection methodology of liquid levelmeters, especially, level sensors in non-nuclear category, to be installed in nuclear energy facilities is developed using linguistic fuzzy approaches such as fully-linguistic and semi-linguistic methods. Depending on defuzzification techniques, the linguistic fuzzy methodology leads to either linguistic (exactly, fully-linguistic) or cardinal (i.e., semi-linguistic) evaluation. For the linguistic method, for each alternative, fuzzy preference index is converted to linguistic utility value by means of a similarity measure determining the degree of similarity between fuzzy index and linguistic ratings. For the cardinal method, the index is translated to cardinal overall utility value. According to these values, alternatives of interest are linguistically or numerically evaluated and a suitable alternative can be selected. Under given selection criteria, the suitable selections out of some liquid levelmeters for nuclear facilities are dealt with using the linguistic fuzzy methodology proposed. Then, linguistic fuzzy evaluation results are compared with qualitative result available in the literature. It is found that as to a suitable option the linguistic fuzzy selection is in agreement with the qualitative selection. Additionally, the comparative study shows that the fully-linguistic method using adequate scale system facilitates linguistic interpretation regarding evaluation results.

• 제어로봇시스템학회:학술대회논문집
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• 1997.10a
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• pp.732-735
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• 1997

Variable Structure Controller(VSC) is usually known to have robustness to bounded exogenous disturbances. The robustness is attributed to the discontinuous term in the control input. However, this discontinuous term also causes an undesirable effect called chattering. To alleviate chattering, a hybrid controller consisting of VSC and Fuzzy Logic Controller(FLC) is proposed, which belongs to the category of Fuzzy Sliding Mode Controller(FSMC). The role of FLC in FSMC is to replace a fixed gain of a discontinuous term with a time-varying one based on a specified rule base. The characteristics of proposed controller are shown to be similar to those of VSC with a saturation function instead of sign function. The only remarkable difference is the nonlinearity whose form can be adjusted by free parameters, normalize gain, denormalize gain, and membership functions. Applied to AC servo motor, the proposed controller is compared with VSC in a regulation problem as well as a speed tracking problem. The simulation results show a substantial chatter reduction.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2001.12a
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• pp.279-282
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• 2001

This paper presents an image contrast enhancement technique for improving the low contrast images using the improved IAFC(Integrated Adaptive Fuzzy Clustering) Model. The low pictorial information of a low contrast image is due to the vagueness or fuzziness of the multivalued levels of brightness rather than randomness. Fuzzy image processing has three main stages, namely, image fuzzification, modification of membership values, and image defuzzification. Using a new model of automatic crossover point selection, optimal crossover point is selected automatically. The problem of crossover point selection can be considered as the two-category classification problem. The improved MEC can classify the image into two classes with unsupervised teaming rule. The proposed method is applied to some experimental images with 256 gray levels and the results are compared with those of the histogram equalization technique. We utilized the index of fuzziness as a measure of image quality. The results show that the proposed method is better than the histogram equalization technique.