• Journal of Korea Multimedia Society
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• v.7 no.6
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• pp.841-850
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• 2004

This paper proposes a GA and GDM-based method for removing unnecessary rules and generating relevant rules from the fuzzy rules corresponding to several fuzzy partitions. The aim of proposed method is to find a minimum set of fuzzy rules that can correctly classify all the training patterns. When the fine fuzzy partition is used with conventional methods, the number of fuzzy rules has been enormous and the performance of fuzzy inference system became low. This paper presents the application of GA as a means of finding optimal solutions over fuzzy partitions. In each rule, the antecedent part is made up the membership functions of a fuzzy set, and the consequent part is made up of a real number. The membership functions and the number of fuzzy inference rules are tuned by means of the GA, while the real numbers in the consequent parts of the rules are tuned by means of the gradient descent method. It is shown that the proposed method has improved than the performance of conventional method in formulating and solving a combinatorial optimization problem that has two objectives: to maximize the number of correctly classified patterns and to minimize the number of fuzzy rules.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.59 no.5
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• pp.981-989
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• 2010

In this study, we introduce a new architecture of fuzzy inference system. In the fuzzy inference system, we use Fuzzy C-Means clustering algorithm to form the premise part of the rules. The membership functions standing in the premise part of fuzzy rules do not assume any explicit functional forms, but for any input the resulting activation levels of such radial basis functions directly depend upon the distance between data points by means of the Fuzzy C-Means clustering. As the consequent part of fuzzy rules of the fuzzy inference system (being the local model representing input output relation in the corresponding sub-space), four types of polynomial are considered, namely constant, linear, quadratic and modified quadratic. This offers a significant level of design flexibility as each rule could come with a different type of the local model in its consequence. Either the Least Square Estimator (LSE) or the weighted Least Square Estimator (WLSE)-based learning is exploited to estimate the coefficients of the consequent polynomial of fuzzy rules. In fuzzy modeling, complexity and interpretability (or simplicity) as well as accuracy of the obtained model are essential design criteria. The performance of the fuzzy inference system is directly affected by some parameters such as e.g., the fuzzification coefficient used in the FCM, the number of rules(clusters) and the order of polynomial in the consequent part of the rules. Accordingly we can obtain preferred model structure through an adjustment of such parameters of the fuzzy inference system. Moreover the comparative experimental study between WLSE and LSE is analyzed according to the change of the number of clusters(rules) as well as polynomial type. The superiority of the proposed model is illustrated and also demonstrated with the use of Automobile Miles per Gallon(MPG), Boston housing called Machine Learning dataset, and Mackey-glass time series dataset.

• Journal of the Korean Data and Information Science Society
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• v.19 no.3
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• pp.925-936
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• 2008

An association rule mining finds the relation among each items in massive volume database. In generating association rules, the researcher specifies the measurements randomly such as support, confidence and lift, and produces the rules. The rule is not produced if it is not suitable to the one any condition which is given value. For example, in case of a little small one than the value which a confidence value is specified but a support and lift's value is very high, this rule is meaningful rule. But association rule mining can not produce the meaningful rules in this case because it is not suitable to a given condition. Consequently, we creat insignificant error which is not selected to the meaningful rules. In this paper, we suggest clustering technique to association rule measures for finding effective association rules using measure of association.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.13 no.11
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• pp.5379-5388
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• 2012

In fuzzy modeling for nonlinear process, the fuzzy rules are typically formed by selection of the input variables, the number of space division and membership functions. The Generation of fuzzy rules for nonlinear processes have the problem that the number of fuzzy rules exponentially increases. To solve this problem, complex nonlinear process can be modeled by generating the fuzzy rules by means of fuzzy division of input space. Therefore, in this paper, rules of non-fuzzy inference systems are generated by partitioning the input space in the scatter form using HCM clustering algorithm. The premise parameters of the rules are determined by membership matrix by means of HCM clustering algorithm. The consequence part of the rules is represented in the form of polynomial functions and the consequence parameters of each rule are identified by the standard least-squares method. And lastly, we evaluate the performance and the nonlinear characteristics using the data widely used in nonlinear process. Through this experiment, we showed that high-dimensional nonlinear systems can be modeled by a very small number of rules.

• International journal of advanced smart convergence
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• v.2 no.1
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• pp.12-17
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• 2013

This paper introduces the fuzzy scatter partition-based fuzzy inference system to construct the model for nonlinear process to analyze nonlinear characteristics. The fuzzy rules of fuzzy inference systems are generated by partitioning the input space in the scatter form using Fuzzy C-Means (FCM) clustering algorithm. The premise parameters of the rules are determined by membership matrix by means of FCM clustering algorithm. The consequence part of the rules is represented in the form of polynomial functions and the parameters of the consequence part are estimated by least square errors. The proposed model is evaluated with the performance using the data widely used in nonlinear process. Finally, this paper shows that the proposed model has the good result for high-dimension nonlinear process.

• The Korean Journal of Applied Statistics
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• v.17 no.1
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• pp.135-144
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• 2004

We propose a reproducibility (validity) assessment procedure of K-means cluster analysis by randomly partitioning the data set into three parts, of which two subsets are used for developing clustering rules and one subset for testing consistency of clustering rules. Also, as an alternative to Rand index and corrected Rand index, we propose an entropy-based consistency measure between two clustering rules, and apply it to determination of the number of clusters in K-means clustering.

• Journal of Arbitration Studies
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• v.24 no.3
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• pp.33-46
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• 2014

Amiable composition is a means of dispute resolution based on the arbitrator's authority to base his decision on equity. Although this method has been used frequently in the last decades of the 20th Century, the number of the published awards by amiable compositeur arbitrators is getting lower and lower. The reason(s) for unpopularity of amiable composition should be sought in its very nature, in its relationships with other institutions such as arbitration in law, equity, ex aequo et bono arbitration, other means of dispute resolution and in its role in the development of the rules specific to international commerce. A brief look at the history of law shows that the concept of equity comes to the scene every time that the rigidity of the rules of law challenges the justice. This has been the case in the 20th Century with respect to international commercial law which was deprived of specific rules. The role of amiable composition has been to contribute to the development of the rules specific to international commerce. The progressive codification of such rules in the last decades is also owed to amiable composition, which has accomplished its mission in the evolution of these rules.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.11
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• pp.2108-2116
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• 2008

The paper concerns Fuzzy C-Means clustering based Radial Basis Function neural networks (FCM-RBFNN) and the optimization of the network is carried out by means of Particle Swarm Optimization(PSO). FCM-RBFNN is the extended architecture of Radial Basis Function Neural Network(RBFNN). 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 - RBFNN model, the order of four types of polynomials can be considered such as constant, linear, quadratic and modified quadratic. Weighted Least Square Estimator(WLSE) are used to estimates the coefficients of polynomial. Since the performance of FCM-RBFNN is affected by some parameters of FCM-RBFNN 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 PSO is exploited to carry out the structural as well as parametric optimization of FCM-RBFNN. Moreover The proposed model is demonstrated with the use of numerical example and gas furnace data set.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1998.06a
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• pp.387-390
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• 1998

In this paper, we suggested a neuro-fuzzy learning algorithm for tuning fuzzy rules, in which a fuzzy system model is of additive-type. Using the method, it is possible to reduce the computation size, since performing the fuzzy inference and tuning the fuzzy rules of each fuzzy subsystem model are independent. Moreover, the efficiency of suggested method is shown by means of a numerical example.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.14 no.1
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• pp.378-384
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• 2013

In this paper, we propose the fuzzy neural networks based on fuzzy c-means clustering algorithm. Typically, the generation of fuzzy rules have the problem that the number of fuzzy rules exponentially increases when the dimension increases. To solve this problem, the fuzzy rules of the proposed networks are generated by partitioning the input space in the scatter form using FCM clustering algorithm. The premise parameters of the fuzzy rules are determined by membership matrix by means of FCM clustering algorithm. The consequence part of the rules is expressed in the form of polynomial functions and the learning of fuzzy neural networks is realized by adjusting connections of the neurons, and it follows a back-propagation algorithm. The proposed networks are evaluated through the application to nonlinear process.