• Journal of applied mathematics & informatics
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• v.20 no.1_2
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• pp.345-354
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• 2006

In this paper first, we find a canonical symmetrical trapezoidal(triangular) for the solution of the fuzzy linear system $A\tilde{x}=\tilde{b}$, where the elements in A and $\tilde{b}$ are crisp and arbitrary fuzzy numbers, respectively. Then, a model for fuzzy linear programming problem with fuzzy variables (FLPFV), in which, the right hand side of constraints are arbitrary numbers, and coefficients of the objective function and constraint matrix are regarded as crisp numbers, is discussed. A numerical procedure for calculating a canonical symmetrical trapezoidal representation for the solution of fuzzy linear system and the optimal solution of FLPFV, (if there exist) is proposed. Several examples illustrate these ideas.

• 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.

• 제어로봇시스템학회:학술대회논문집
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• 2003.10a
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• pp.2393-2398
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• 2003

In this paper, we proposes a new fuzzy inference system for modeling nonlinear systems given input and output data. In the suggested fuzzy inference system, the number of fuzzy rules and parameter values of membership functions are automatically decided by using the kernel-based method. The kernel-based method individually performs linear transformation and kernel mapping. Linear transformation projects input space into linearly transformed input space. Kernel mapping projects linearly transformed input space into high dimensional feature space. The structure of the proposed fuzzy inference system is equal to a Takagi-Sugeno fuzzy model whose input variables are weighted linear combinations of input variables. In addition, the number of fuzzy rules can be reduced under the condition of optimizing a given criterion by adjusting linear transformation matrix and parameter values of kernel functions using the gradient descent method. Once a structure is selected, coefficients in consequent part are determined by the least square method. Simulated result illustrates the effectiveness of the proposed technique.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2000.11a
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• pp.191-194
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• 2000

In this paper, an output tracking control technique of discrete-time Takagi-Sugeno (TS) fuzzy systems is developed. The TS fuzzy system is represented as an uncertain multiple linear system. The tracking problem of TS fuzzy system is converted into the stabilization problem of a uncertain multiple linear system. A sufficient condition for asymptotic tracking is obtained in terms of linear matrix inequalities (LMI). A design example is illustrated to show the effectiveness of the proposed method.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2000.05a
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• pp.260-263
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• 2000

In this paper, a tracking control technique of Takagi-Sugeno(TS) fuzzy systems with parametric uncertainties is developed. The uncertain TS fuzzy system is represented as an uncertain multiple linear system. The tracking problem of TS fuzzy system is converted into the regulation problem of a multiple linear system. A sufficient condition for robust tracking is obtained in terms of linear matrix inequalities(LMI). A Design example is illustrated to show the effectiveness of the proposed method.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.57 no.9
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• pp.1642-1651
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• 2008

The dynamic behavior of power systems is affected by the interactions between linear and nonlinear components. To analyze those complicated power systems, the linear approaches have been widely used so far. Especially, a synchronous generator has been designed by using linear models and traditional techniques. However, due to its wide operating range, complex dynamics, transient performances, and its nonlinearities, it cannot be accurately modeled as linear methods based on small-signal analysis. This paper describes an application of the Takaki-Sugeno (T-S) fuzzy method to model the synchronous generator in a single-machine infinite bus (SMIB) system. The T-S fuzzy model can provide a highly nonlinear functional relation with a comparatively small number of fuzzy rules. The simulation results show that the proposed T-S fuzzy modeling captures all dynamic characteristics for the synchronous generator, which are exactly same as those by the conventional modeling method.

• Journal of information and communication convergence engineering
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• v.8 no.6
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• pp.702-708
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• 2010

This paper proposes a novel linearization method for Takagi.sugeno (TS) fuzzy model. A T-S fuzzy controller consists of linear controllers based on local linear models and the local linear controllers cannot be designed independently because of overall stability conditions which are usually conservative. To use linear control theories easily for T-S fuzzy system, the linearization of T-S fuzzy model is required. However, The linearization of T-S fuzzy model is difficult to be achieved by using existing linearization methods because fuzzy rules and membership functions are included in T-S fuzzy models. So, a new linearization method is proposed for the T-S fuzzy system based on the idea of T-S fuzzy state transformation. For the T-S fuzzy system linearized with uncertainties, a robust optimal controller with the robustness of sliding model control(SMC) is designed.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.12 no.20
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• pp.97-104
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• 1989

In this thesis, each objective functions with hierarchical system Bi-level linear programming (BLPP) Problem applications to fuzzy set theory conducted multiple objective programming problem. Using linear fuzzy membership functions make a change typical BLPP and presents modified method turn to account established BLPP method, presents operation results lead to example. Fuzzy Bi-level linear programming problem (FBLPP) can be natural describe realities of life then BLPP.

• Journal of the Korean Institute of Intelligent Systems
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• v.10 no.3
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• pp.260-269
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• 2000

The fuzzy and state-feedback control systems have been applied in various areas from non-linear to linear systems. A Fuzzy controller is endowed with control rules and membership function that are constructed on the knowledge of expert, as like intuition and experience. but It is very difficult to obtain the exact values which are the membership function and consequent parameters. though apply back-propagation algorithm to the system, the convergence time a much. Besides, the state-feedback system is most widely used in industry due to its simple control structure and easily able to design the controller. but it is weak in complex system of higher degree and non-linear. In this paper presents the design of a fuzzy switching mode, it these two controllers work at different operation conditions, the advantages of both controller can be retained and the disadvantages can be removed. Between the Fuzzy and the State-feedback controlles, the good outputs are selected by the switching mode. Moreover it is powerful in complex system of higher degree and non-linear. In these sense compared with the state-feedback controller, the performance of the proposed controller was improvedin the section of linearization.

• Journal of the Korean Institute of Intelligent Systems
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• v.16 no.3
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• pp.303-308
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• 2006

To solve the rule explosion problem in multi input fuzzy logic system, a method of converting a given fuzzy system to 2 layered hierarchical fuzzy system is presented where the collection of the THEN-parts of the fuzzy rules of given fuzzy system is considered as vectors of fuzzy rule. At the 1 st layer, linearly independent fuzzy rule vectors generated from the given fuzzy logic system are used and, at the 2nd layer, linear combinations of these independent fuzzy rule vectors are used for fuzzy logic units at each layer. The resultant 2 layered hierarchical fuzzy system has not only equivalent approximation capability, but less number of fuzzy rules compared with the conventional fuzzy logic system.