• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.3
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• pp.466-472
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• 2008

The paper concerns Fuzzy C-Means clustering based fuzzy neural networks (FCM-FNN) and the optimization of the network is carried out by means of hierarchal fair competition-based parallel genetic algorithm (HFCPGA). FCM-FNN is the extended architecture of Radial Basis Function Neural Network (RBFNN). FCM algorithm is used to determine centers and widths of RBFs. In the proposed network, the membership functions of the premise part of fuzzy rules do not assume any explicit functional forms such as Gaussian, ellipsoidal, triangular, etc., so its resulting fitness values directly rely on the computation of the relevant distance between data points by means of FCM. Also, as the consequent part of fuzzy rules extracted by the FCM-FNN model, the order of four types of polynomials can be considered such as constant, linear, quadratic and modified quadratic. Since the performance of FCM-FNN is affected by some parameters of FCM-FNN such as a specific subset of input variables, fuzzification coefficient of FCM, the number of rules and the order of polynomials of consequent part of fuzzy rule, we need the structural as well as parametric optimization of the network. In this study, the HFCPGA which is a kind of multipopulation-based parallel genetic algorithms(PGA) is exploited to carry out the structural optimization of FCM-FNN. Moreover the HFCPGA is taken into consideration to avoid a premature convergence related to the optimization problems. The proposed model is demonstrated with the use of two representative numerical examples.

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.7
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• pp.889-894
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• 2004

The fuzzy kernel c-means (FKCM) algorithm, which uses a kernel function, can obtain more desirable clustering results than fuzzy c-means (FCM) for not only spherical data but also non-spherical data. However, it can be sensitive to noise as in the FCM algorithm. In this paper, a kernel function is applied to the possibilistic c-means (PCM) algorithm and is shown to be robust for data with additive noise. Several experimental results show that the proposed kernel possibilistic c-means (KPCM) algorithm out performs the FKCM algorithm for general data with additive noise.

• Proceedings of the KIEE Conference
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• 2008.10b
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• pp.239-240
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• 2008

본 논문에서는 Subtractive clustering 알고리즘을 이용한 Fuzzy Radial Basis Function Neural Network (FRBFNN)의 규칙 수를 자동적으로 생성하는 방법을 제시한다. FRBFNN은 멤버쉽 함수로써 기존 RBFNN에서 가우시안이나 타원형 형태의 특정 RBF를 사용하는 구조와 달리 Fuzzy C-Means clustering 알고리즘에서 사용하는 거리에 기한 멤버쉽 함수를 사용하여 전반부의 공간 분할 및 활성화 레벨을 결정하는 구조이다. 본 논문에서는 데이터의 밀집도에 기반을 두어 클러스터링을 하는 Subtractive clustering 알고리즘을 사용하여 퍼지 규칙의 수와 같은 의미를 갖는 분할할 입력공간의 수와 분할된 입력공간의 중심값을 동정하며, Least Square Estimator (LSE) 알고리즘을 사용하여 후반부 다항식의 계수를 추정 한다.

• Proceedings of the KIEE Conference
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• 2005.10b
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• pp.146-148
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• 2005

In this paper, we propose a genetically optimized identification of information granulation(IG)-based fuzzy model. To optimally design the IG-based fuzzy model we exploit a hybrid identification through genetic alrogithms(GAs) and Hard C-Means (HCM) clustering. An initial structure of fuzzy model is identified by determining the number of input, the seleced input variables, the number of membership function, and the conclusion inference type by means of GAs. Granulation of information data with the aid of Hard C-Means(HCM) clustering algorithm help determine the initial paramters of fuzzy model such as the initial apexes of the membership functions and the initial values of polyminial functions being used in the premise and consequence part of the fuzzy rules. And the inital parameters are tuned effectively with the aid of the genetic algorithms and the least square method. And also, we exploite consecutive identification of fuzzy model in case of identification of structure and parameters. Numerical example is included to evaluate the performance of the proposed model.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.60 no.11
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• pp.2157-2164
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• 2011

In this paper, we introduce a new category of fuzzy inference system based on Type-2 fuzzy c-means clustering algorithm (T2FCM-based FIS). The premise part of the rules of the proposed model is realized with the aid of the scatter partition of input space generated by Type-2 FCM clustering algorithm. The number of the partition of input space is composed of the number of clusters and the individual partitioned spaces describe the fuzzy rules. Due to these characteristics, we can alleviate the problem of the curse of dimensionality. The consequence part of the rule is represented by polynomial functions with interval sets. To determine the structure and estimate the values of the parameters of Type-2 FCM-based FIS we consider the successive tuning method with generation-based evolution by means of real-coded genetic algorithms. The proposed model is evaluated with the use of numerical experimentation.

• Kyungpook Mathematical Journal
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• v.50 no.3
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• pp.411-417
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• 2010

Some characterizations of regular $\Gamma$-rings are described by means of fuzzy ideals. The concepts of fuzzy interior ideals in $\Gamma$-rings and semisimple $\Gamma$-rings are introduced. Some characterizations of semisimple $\Gamma$-rings are investigated by means of fuzzy interior ideals.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.10 no.1
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• pp.89-93
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• 2010

In this paper a new fuzzy clustering approach to the color clustering problem has been proposed. To deal with the limitations of the traditional FCM algorithm, we propose a spatial homogeneity-based FCM algorithm. Moreover, the cluster validity index is employed to automatically determine the number of clusters for a given image. We refer to this method as VS-FCM algorithm. The effectiveness of the proposed method is demonstrated through various clustering examples.

• Journal of the Korean Institute of Intelligent Systems
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• v.2 no.3
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• pp.40-49
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• 1992

In this paper, an approach to identify fuzzy rules is proposed. The decision of the optimal number of fuzzy rule is made by means of fuzzy c-means clustering. The identification of the parameters of fuzzy implications is carried out by use of genetic algorithms. For the efficinet and fast parameter identification, the reduction thechnique of search areas of genetica algorithms is proposed. The feasibility of the proposed approach is evaluated through the identification of the fuzzy model to describe an input-output relation of Gas Furnace. Despite the simplicity of the propsed apprach the accuracy of the identified fuzzy model of gas furnace is superior as compared with that of other fuzzy modles.

• Journal of the Korean Institute of Intelligent Systems
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• v.27 no.2
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• pp.99-105
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• 2017

Type-2 fuzzy sets are preferred over type-1 sets as they are capable of addressing uncertainty more efficiently. The fuzzifier values play pivotal role in managing these uncertainties; still selecting appropriate value of fuzzifiers has been a tedious task. Generally, based on observation particular value of fuzzifier is chosen from a given range of values. In this paper we have tried to adaptively compute suitable fuzzifier values of interval type-2 possibilistic fuzzy c-means (IT2 PFCM) for a given data. Information is extracted from individual data points using histogram approach and this information is further processed to give us the two fuzzifier values $m_1$, $m_2$. These obtained values are bounded within some upper and lower bounds based on interval type-2 fuzzy sets.

• Journal of the Korean Institute of Intelligent Systems
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• v.14 no.5
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• pp.517-524
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• 2004

The fuzzy set theory has been wide used in clustering of machine learning with data mining since fuzzy theory has been introduced in 1960s. In particular, fuzzy C-means algorithm is a popular fuzzy clustering algorithm up to date. An element is assigned to any cluster with each membership value using fuzzy C-means algorithm. This algorithm is affected from the location of initial cluster center and the proper cluster size like a general clustering algorithm as K-means algorithm. This setting up for initial clustering is subjective. So, we get improper results according to circumstances. In this paper, we propose a cluster merging using enhanced density based fuzzy C-means clustering algorithm for solving this problem. Our algorithm determines initial cluster size and center using the properties of training data. Proposed algorithm uses grid for deciding initial cluster center and size. For experiments, objective machine learning data are used for performance comparison between our algorithm and others.