• Journal of the Chungcheong Mathematical Society
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• v.23 no.3
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• pp.563-570
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• 2010

In this article, we take account of the fuzzy stability for generalized derivation in fuzzy Banach algebra.

• Korean Journal of Mathematics
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• v.22 no.4
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• pp.659-670
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• 2014

In this paper, we prove the Hyers-Ulam stability of homomorphisms in fuzzy Banach algebras and of derivations on fuzzy Banach algebras associated to the Cauchy-Jensen functional equation.

• Journal of the Korean Institute of Intelligent Systems
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• v.7 no.2
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• pp.3-15
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• 1997

In order to apply fuzzy logic, two major tasks need to be performed: the derivation of fuzzy rules and the determination of membership functions. These tasks are often difficult and time-consuming. This paper presents an algorithmic method for generating membership functions and fuzzy rules applicable to decision-making problems; the method includes an entropy minimization for clustering analog samples. Membership functions are derived by partitioning the variables into desired number of fuzzy terms, and fuzzy rules are obtained using minimum entropy clustering. In the mle derivation process, rule weights are also calculated. Inference and defuzzification for classification problems are also discussed.

• Journal of Electrical Engineering and information Science
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• v.2 no.6
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• pp.191-196
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• 1997

Fuzzy clustering has been playing an important role in solving many problems. Fuzzy c-Means(FCM) algorithm is most frequently used for fuzzy clustering. But some fixed point of FCM algorithm, know as Tucker's counter example, is not a reasonable solution. Moreover, FCM algorithm is impossible to perform the on-line learning since it is basically a batch learning scheme. This paper presents unsupervised learning networks as an attempt to improve shortcomings of the conventional clustering algorithm. This model integrates optimization function of FCM algorithm into unsupervised learning networks. The learning rule of the proposed scheme is a result of formal derivation based on the gradient descent procedure of a fuzzy objective function. Using the result of formal derivation, two algorithms of fuzzy cluster analysis, the batch learning version and on-line learning version, are devised. They are tested on several data sets and compared with FCM. The experimental results show that the proposed algorithms find out the reasonable solution on Tucker's counter example.

• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.8
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• pp.720-725
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• 2001

Derivation of TSK fuzzy model from nonlinear differential equation is fundamental issue in the field of theoretical fuzzy control. The method which does not yield affine local differential equations at off-equilibrium points is proposed in this paper. A prototype TSK fuzzy model which has triangular membership functions for linguistic terms of the antecedent part is derived systematically. And then GA is used to modify the membership functions optimally. Simulation results show the validity of the proposed method.

• Proceedings of the IEEK Conference
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• 2002.07c
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• pp.1483-1486
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• 2002

In this paper, a new scheme of iterative loaming control of a robot manipulator is presented. The proposed method uses a fuzzy sliding mode controller(FSMC), which is designed based on the similarity between the fuzzy logic control(FLC) and the sliding mode control(SMC), for the feedback. With this, the proposed method makes possible fDr fast iteration and has advantages that no linear approximation is used for the derivation of the learning law or in the stability proof Full proof of the convergence of the fuzzy sliding base learning scheme Is given.

• 제어로봇시스템학회:학술대회논문집
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• 1992.10a
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• pp.441-446
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• 1992

We propose a control architecture for the fuzzy logic control of robot manipulators and a rule base derivation method for a fuzzy logic controller(FLC) using a neural network. The control architecture is composed of FLC and PD(positional Derivative) controller. And a neural network is designed in consideration of the FLC's structure. After the training is finished by BP(Back Propagation) and FEL(Feedback Error Learning) method, the rule base is derived from the neural network and is reduced through two stages - smoothing, logical reduction. Also, we show the performance of the control architecture through the simulation to verify the effectiveness of our proposed method.

• Journal of the Korean Institute of Intelligent Systems
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• v.5 no.4
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• pp.87-100
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• 1995

In order to control systems which contain nonlinearities of uncertainties, control strategies must deal with the effects of them. Since most of control methods based on system mathematical models have been mainly developed focused on stability robustness against nonlinearities or uncertainties under the assumption that controlled systems are linear time invariant, they have certain amount of limitations to smartly improve the transient responses of systems disturbed by nonlinearities or uncertainties. In this paper, a nonlinear fuzzy PID control method is suggested which can stably improve the transient responses of systems disturbed by nonlinearities, as well as systems whose mathematical characteristics are not perfectly known. Although the derivation process is based on the design process similar to general fuzzy logic controller, resultant control law has analytical forms with time varying PID gains rather than linguistic forms, so that implementation using common-used versatile microprocessors cna be achieved easily and effectively in real-time control aspect.

• Journal of Advanced Marine Engineering and Technology
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• v.36 no.7
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• pp.927-934
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• 2012

This paper suggests a new fuzzy PID controller with variable parameters which improves the shortage of the fuzzy PID controller with fixed parameters suggested in [9]. The derivation procedure follows the general design procedure of the fuzzy logic controller, while the resultant control law is the form of the conventional PID controller. Therefore, the suggested controller has two advantages. One is that it has only four fuzzy linguistic rules and analytical form of control laws so that the real-time control system can be implemented based on low-price microprocessors. The other is that the PID control action can always be achieved with time-varying PID controller gains only by adjusting the input and output scalers at each sampling time.

• Proceedings of the Korean Society of Marine Engineers Conference
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• 2001.05a
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• pp.238-242
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• 2001

In this paper, we proposed an optimal identification method of the membership functions and the numbers of fuzzy rule base for the stabilization controller of the Thermal process control system by RVEGA. Although fuzzy logic controllers and expert systems have been successfully applied in many complex industrial process, they must rely on experts knowledges. So it is difficult in determination of the linguistic state space, definition of the membership functions of each linguistic term and the derivation of the control rules. To verify the validity of this RVEGA-based fuzzy controller, Thermal process control system, with strong nonlinear dynamics, was selected for application of this algorithm and compare with PI controller, and the empirically improved fuzzy controller.