• Journal of the Korean Institute of Intelligent Systems
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• v.5 no.1
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• pp.15-20
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• 1995

Fuzzy membership functions are some kinds of mapping function for the fuzzification and the defuzzification. Triangle-shaped fuzzy membership functions are widely used in fuzzy controller, for it is easy to implement. In these membership functions, it is known that narrower fuzzy sets permit finer control near the operating point than that far from the operating point. $Supp{\acute{o}}se$ we have a membership function with narrower triangle near zero and wider triangle far from zero. The membership function will make fine control when small input is given and rough control at large input. Therefore the performance of the controller with that membership function will be enhanced. This paper presents how the width of triangle base in the fuzzy membership function has influence on the output using geometrical approaches.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2007.11a
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• pp.183-186
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• 2007

We introduction some properties for fuzzy power function of performance of a test. First we define fuzzy type I error and type II error for the probability of the two types of error. And we show that an fuzzy error probability of one kind can only be reduced at cost of increasing the other fuzzy error probability.

• Proceedings of the KIEE Conference
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• 1998.07g
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• pp.2203-2205
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• 1998

This paper describes fuzzy radial basis function networks(FRBFN) extracting fuzzy rules through the learning from training data set. The proposed FRBFN is derived from the functional equivalence between RBF networks and fuzzy inference systems. The FRBFN learn by assigning new fuzzy rules and updating the parameters of existing fuzzy rules. The parameters of the FRBFN are adjusted using the standard LMS algorithm. The performance of the FRBFN is illustrated with function approximation and system identification.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2007.11a
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• pp.199-202
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• 2007

The similarity measure is constructed for non-convex fuzzy membership function using well known Hamming distance measure. Comparison with convex fuzzy membership function is carried out, furthermore characteristic analysis for non-convex function are also illustrated. Proposed similarity measure is proved and the usefulness is verified through example. In example, usefulness of proposed similarity is pointed out.

• The Transactions of The Korean Institute of Electrical Engineers
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• v.58 no.6
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• pp.1223-1229
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• 2009

The performance of Radial Basis Function Neural Networks depends on setting up the Radial Basis Functions over the input space which are the important design procedure of Radial Basis Function Neural Networks. The existing method to initialize the location of the radial basis functions over the input space is to use the conditional fuzzy C-means clustering. However, the researchers which are interested in the conditional fuzzy C-means clustering cannot get as good modeling performance as they expect because the conditional fuzzy C-means clustering cannot project the information which is extracted over the output space into the input space. To compensate the above mentioned drawback of the conditional fuzzy C-means clustering, we apply a fuzzy K-nearest neighbors approach to project the auxiliary information defined over the output space into the input space without lose of the information.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.3 no.1
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• pp.13-17
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• 2003

A continuous solution of the Dirichlet boundary value problem for the heat equation $u_t$＝$a2u_{xx}$ using a fuzzy system is described. We first apply the Crank-Nicolson method to obtain a discrete solution at the grid points for the heat equation. Then we find a continuous function to represent approximately the discrete values at the grid points in the form of a bicubic spline function (equation omitted) that can in turn be represented exactly by a fuzzy system. We show that the computed values at non-grid points using the bicubic spline function is much smaller than the ones obtained by linear interpolations of the values at the grid points. We also show that the fuzzy rule table in the fuzzy system representation of the bicubic spline function can be viewed as a gray scale image. Hence, the fuzzy rules provide a visual representation of the functions of two variables where the contours of different levels for the function are shown in different gray scale levels

• Nonlinear Functional Analysis and Applications
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• v.26 no.3
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• pp.513-530
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• 2021

The purpose of this paper is to introduce and study a class of coupled systems of fuzzy delay differential equations involving fuzzy initial values and fuzzy source functions of triangular type. We assume that these initial values and source functions are triangular fuzzy functions and define solutions of the coupled systems as a triangular fuzzy function matrix consisting of real functional matrices. The method of triangular fuzzy function, fractional steps and fuzzy terms separation are used to solve the problems. Furthermore, we prove existence and uniqueness of solution for the considered systems, and then a solution algorithm is proposed. Finally, we present an example to illustrate our main results and give some work that can be done later.

• Proceedings of the Korea Association of Information Systems Conference
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• 1996.11a
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• pp.211-216
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• 1996

This paper propose a fuzzy regression method using fuzzy neural networks when a membership value is attached to each input-output pair. First, an architecture o fuzzy neural networks with fuzzy weights and fuzzy biases is shown. Next, a cost function is defined using the fuzzy output from the fuzzy neural network and the corresponding target output with a membership value. A learning algorithm is derived from the cost function. The derived learning algorithm trains the fuzzy neural network so 솜 t the level set of the fuzzy output includes the target output. Last, the proposed method is applied to the quality evaluation problem of injection molding

• Proceedings of the Korea Society for Industrial Systems Conference
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• 1996.10a
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• pp.211-216
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• 1996

This paper propose a fuzzy regression method using fuzzy neural networks when a membership value is attached to each input-output pair. First, an architecture of fuzzy nerual networks with fuzzy weights and fuzzy biases is shown. Next a cost function is defined using the fuzzy output from the fuzzy neural network and the corresponding target output with a membership value.A learning algorithm is derived from the cost function. The derived learning algorithm trains the fuzzy neural network so that the level set of the fuzzy output includes the target output. Last, the proposed method is applied to the quality evaluation problem of injection molding.

• Management & Information Systems Review
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• v.9
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• pp.25-39
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• 2002

We consider the Fuzzy clustering which is devised for partitioning a set of objects into a certain number of groups by assigning the membership probabilities to each object. The researches carried out in this field before show that the Fuzzy clustering concept is involved so much that for a certain set of data, the main purpose of the clustering cannot be attained as desired. Thus we propose a new objective function, named as Fuzzy-Entroppy Function in order to satisfy the main motivation of the clustering which is classifying the data clearly. Also we suggest Mean Field Annealing Algorithm as an optimization algorithm rather than the. ISODATA used traditionally in this field since the objective function is changed. We show the Mean Field Annealing Algorithm works pretty well not only for the new objective function but also for the classical Fuzzy objective function by indicating that the local minimum problem resulted from the ISODATA can be improved.