• The Pure and Applied Mathematics
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• v.27 no.1
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• pp.35-42
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• 2020

In this paper, numerical algorithms for solving a fuzzy system of linear equations with crisp coefficients are presented. We illustrate the efficiency and accuracy of the proposed methods by solving some numerical examples. We also provide a graphical representation of the fuzzy solutions in three-dimension as a visual reference of the solution of the fuzzy system.

• Coupled systems mechanics
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• v.1 no.4
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• pp.345-360
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• 2012

In this article we have presented a unique representation for interval arithmetic. The traditional interval arithmetic is transformed into crisp by symbolic parameterization. Then the proposed interval arithmetic is extended for fuzzy numbers and this fuzzy arithmetic is used as a tool for uncertain finite element method. In general, the fuzzy finite element converts the governing differential equations into fuzzy algebraic equations. Fuzzy algebraic equations either give a fuzzy eigenvalue problem or a fuzzy system of linear equations. The proposed methods have been used to solve a test problem namely heat conduction problem along with fuzzy finite element method to see the efficacy and powerfulness of the methodology. As such a coupled set of fuzzy linear equations are obtained. These coupled fuzzy linear equations have been solved by two techniques such as by fuzzy iteration method and fuzzy eigenvalue method. Obtained results are compared and it has seen that the proposed methods are reliable and may be applicable to other heat conduction problems too.

• Journal of Institute of Control, Robotics and Systems
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• v.17 no.9
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• pp.897-901
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• 2011

This paper presents a TS (Takagi-Sugeno) type FLC (Fuzzy Logic Controller) with only 3 rules. The choice of parameters of FLC is very difficult job on design FLC controller. Therefore, the choice of appropriate linguistic variable is an important part of the design of fuzzy controller. However, since fuzzy controller is nonlinear, it is difficult to analyze mathematically the affection of the linguistic variable. So this choice is depend on the expert's experience and trial and error method. In the design of the system, we use a variety of response characteristics like stability, rising time, overshoot, settling time, steady-state error. In particular, it is important for a stable system design to predict the steady-state error because the system's steady-state response of the system is related to the overall quality. In this paper, we propose the method to choose the consequence linear equation's parameter of T-S type FLC in the view of steady-state error. The parameters of consequence linear equations of FLC are tuned according to the system error that is the input of FLC. The full equation of T-S type FLC is presented and using this equation, the relation between output and parameters can represented. As well as the FLC parameters of consequence linear equations affect the stability of the system, it also affects the steady-state error. In this study, The system according to the parameter of consequence linear equations of FLC predict the steady-state error and the method to remove the system's steady-state error is proposed using the prediction error value. The simulation is carried out to determine the usefulness of the proposed method.

• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.97-118
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• 2006

We obtain a property of distributivity in the equivalence form over LR fuzzy intervals. As an application and main result of the paper, we give a determinant method to solve systems of linear equivalentions. The expected value of the obtained solution is equal to the corresponding solution of the classical system of linear equations considering the expected values as data.

• Proceedings of the KIEE Conference
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• 2000.11d
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• pp.697-699
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• 2000

In this paper, an extension of model predictive controller for nonlinear process using Takagi-Sugeno(TS) fuzzy model is proposed Since the consequent parts of TS fuzzy model comprise linear equations of input and output variables. it is locally linear, and the Generalized Predictive Control(GPC) technique which has been developed to control Linear Time Invariant(LTI) plants, can be extended as a parallel distributed controller. Also fuzzy soft constraints are introduced to handle both equality and inequality constraints in a unified form. So the traditional constrained GPC can be transferred to a standard fuzzy optimization problem. The proposed method conciliates the advantages of the fuzzy modeling with the advantages of the constrained predictive control, and the degree of freedom is increased in specifying the desired process behavior.

• 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.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 1993.06a
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• pp.1090-1093
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• 1993

In this paper, the design technique of fuzzy controller using pole placement method and the stability analysis of the system are discussed. The consequent parts of the fuzzy model representing the fuzzy control system are descrived by linear stated equations. It cannot be guaranteed that the total fuzzy system is stable even if all subsystems are stable. The range of the consequent parameters of fuzzy feedback controller which is stable for each fuzzy subspace of the input space are derived, using a rather simplified stability criterion. Then, the consequent parameters of fuzzy controller is determined with the sufficient condition that the fuzzy feedback controller maintain robust stability for the model of other subspace.

• Proceedings of the KIEE Conference
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• 2001.07d
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• pp.1949-1951
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• 2001

This paper deals with the control of a nonlinear experimental helicopter system by using the fuzzy-model-based control approach. The fuzzy model of the experimental helicopter system is constructed from the original nonlinear dynamic equations in the form of an affine Takagi-Sugeno (TS) fuzzy system. In order to design a feasible switching-type fuzzy-model-based controller, the TS fuzzy system is converted to a set of uncertain linear systems, which is used as a basic framework to synthesize the fuzzy-model-based controller.

• Journal of the Korean Institute of Telematics and Electronics S
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• v.35S no.11
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• pp.53-67
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• 1998

This paper suggests a method designing the TSK fuzzy controller based on the TSK fuzzy model, which guarantees the stability of the closed loop system and makes the response of the closed loop system to be a desired one. This paper deals with the general type of TSK fuzzy model of which consequents are affine equations having a constant term. The TSK fuzzy controller suggested in this paper is designed by using the pole placement which developed for the linear systems and makes the closed loop system have the same behavior as a desired linear system. A reference input can be introduced to the suggested TSK fuzzy controller and an integral action also can be introduced. Simulation results reveal that the suggested methods are practically feasible. This paper deals with both the continuous systems and the discrete systems.

• Proceedings of the KIEE Conference
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• 1998.11b
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• pp.675-677
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• 1998

In this paper, we propose the fuzzy inference algorithm with multi-layer structure. MFIS(Multi-layer Fuzzy Inference System) uses PNN(Polynomial Neural networks) structure and the fuzzy inference method. The PNN is the extended structure of the GMDH(Group Method of Data Hendling), and uses several types of polynomials such as linear, quadratic and cubic, as well as the biquadratic polynomial used in the GMDH. In the fuzzy inference method, the simplified and regression polynomial inference methods are used. Here, the regression polynomial inference is based on consequence of fuzzy rules with the polynomial equations such as linear, quadratic and cubic equation. Each node of the MFIS is defined as fuzzy rules and its structure is a kind of neuro-fuzzy structure. We use the training and testing data set to obtain a balance between the approximation and the generalization of process model. Several numerical examples are used to evaluate the performance of the our proposed model.