• School Mathematics
• /
• v.14 no.4
• /
• pp.445-468
• /
• 2012

This study is tried in order to link informal arithmetic reasoning to formal algebraic reasoning. In this study, we investigated elementary school student's non-formal algebraic reasoning used in algebraic problem solving. The result of we investigated algebraic reasoning of 839 students from grade 1 to 6 in two schools, Korea, we could recognize that they used various arithmetic reasoning and pre-formal algebraic reasoning which is the other than that is proposed in the text book in word problem solving related to the linear systems of equation. Reasoning strategies were diverse depending on structure of meaning and operational of problems. And we analyzed the cause of failure of reasoning in algebraic problem solving. Especially, 'quantitative reasoning', 'proportional reasoning' are turned into 'non-formal method of substitution' and 'non-formal method of addition and subtraction'. We discussed possibilities that we are able to connect these pre-formal algebraic reasoning to formal algebraic reasoning.

• Proceedings of the Korean Institute of Information and Commucation Sciences Conference
• /
• 2008.05a
• /
• pp.193-196
• /
• 2008

Z. Cao had proposed NFRM(new fuzzy reasoning method) which infers in detail using relation matrix. In spite of the small inference rules, it shows good performance than mamdani's fuzzy inference method. In this paper, we propose 2. Cao's fuzzy inference method using learning ability witch is used a gradient descent method in order to improve the performances. Because it is difficult to determine the relation matrix elements by trial and error method which is needed many hours and effort. Simulation results are applied linear and nonlinear system show that the proposed inference method has good performances.

• 제어로봇시스템학회:학술대회논문집
• /
• 2000.10a
• /
• pp.68-68
• /
• 2000

This paper presents a fuzzy modified PID controller that uses linear fuzzy inference method. In this structure, the proportional and derivative gains vary with the output of the system under control. 2-input PD type fuzzy controller is designed to obtain the varying gains. The proposed fuzzy PID structure maintains the same performance as the general-purpose linear PID controller, and enhances the tracking performance over a wide range of input. Numerical simulations and experimental results show the effectiveness of the fuzzy PID controller in comparison with the conventional PID controller.

• Proceedings of the KIEE Conference
• /
• 1990.11a
• /
• pp.417-420
• /
• 1990

The conventional quantitative techniques of system analysis are intrinsically unsuited for dealing with humanistic systems. Therefore, the rule based modeling of fuzzy linguistic type has been developed for the analysis of humanistic systems and complex systems and it is very significant for analysis and design of fuzzy logic controller. The activated sludge process is a commonly used method for treating sewage and waste waters. A mathematical tool to build a fuzzy model of the activated sludge process where fuzzy implications and linear reasoning are used is presented in here. A root-mean square error is used as the criterion of the fuzzy model's adequacy to the A.S.P. and the least square method is used for the identification of optimum consequence parameters. A method of modeling of the activated sludge process using its input-output data and simulation results for its application are shown.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.4 no.1
• /
• pp.111-118
• /
• 2004

In this paper, we present a novel approach for the structure of Fuzzy Neural Network(FNN) based on wavelet function and apply this network structure to the solution of the tracking problem for mobile robots. Generally, the wavelet fuzzy model(WFM) has the advantage of the wavelet transform by constituting the fuzzy basis function(FBF) and the conclusion part to equalize the linear combination of FBF with the linear combination of wavelet functions. However, it is very difficult to identify the fuzzy rules and to tune the membership functions of the fuzzy reasoning mechanism. Neural networks, on the other hand, utilize their learning capability for automatic identification and tuning. Therefore, we design a wavelet based FNN structure(WFNN) that merges these advantages of neural network, fuzzy model and wavelet transform. The basic idea of our wavelet based FNN is to realize the process of fuzzy reasoning of wavelet fuzzy system by the structure of a neural network and to make the parameters of fuzzy reasoning be expressed by the connection weights of a neural network. And our network can automatically identify the fuzzy rules by modifying the connection weights of the networks via the gradient descent scheme. To verify the efficiency of our network structure, we evaluate the tracking performance for mobile robot and compare it with those of the FNN and the WFM.

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 2000.05a
• /
• pp.114-117
• /
• 2000

In this paper, Fuzzy Self-organizing Neural Networks(FSONN) based on Fuzzy Neural Networks(FNN) is proposed to overcome some problems, such as the conflict between ovefitting and good generation, and low reliability. The proposed FSONN consists of FNN and SONN. Here, FNN is used as the premise part of FSONN and SONN is the consequnt part of FSONN. The FUN plays the preceding role of FSONN. For the fuzzy reasoning and learning method in FNN, Simplified fuzzy reasoning and backpropagation learning rule are utilized. The number of layers and the number of nodes in each layers of SONN that is based on the GMDH method are not predetermined, unlike in the case of the popular multi layer perceptron structure and can be generated. Also the partial descriptions of nodes can use various forms such as linear, modified quadratic, cubic, high-order polynomial and so on. In this paper, the optimal design procedure of the proposed FSONN is shown in each step and performance index related to approximation and generalization capabilities of model is evaluated and also discussed.

• Journal of the Korean Institute of Intelligent Systems
• /
• v.19 no.2
• /
• pp.273-278
• /
• 2009

The determination of the associated weights in the theory of ordered weighted averaging (OWA) operators is one of the important issue. Recently, Wang and Parkan [Information Sciences 175 (2005) 20-29] proposed a minimax disparity approach for obtaining OWA operator weights and the approach is based on the solution of a linear program (LP) model for a given degree of orness. Recently, Liu [International Journal of Approximate Reasoning, accepted] showed that the minimum variance OWA problem of Fuller and Majlender [Fuzzy Sets and Systems 136 (2003) 203-215] and the minimax disparity OWA problem of Wang and Parkan always produce the same weight vector using the dual theory of linear programming. In this paper, we give an improved proof of the minimax disparity problem of Wang and Parkan while Liu's method is rather complicated. Our method gives the exact optimum solution of OWA operator weights for all levels of orness, $0\leq\alpha\leq1$, whose values are piecewise linear and continuous functions of $\alpha$.

• The Mathematical Education
• /
• v.40 no.1
• /
• pp.93-102
• /
• 2001

The world we live in is called the age of information. Thus communication and computers are doing the central role in it. When one studies the mathematical problem, the use of tools such as computers, calculators and technology is available for all students, and then students are actively engaged in reasoning, communicating, problem solving, and making connections with mathematics, between mathematics and other disciplines. The use of technology extends to include computer algebra systems, spreadsheets, dynamic geometry software and the Internet and help active learning of students by analyzing data and realizing mathematical models visually. In this paper, we explain concepts of transformation, linear transformation, congruence transformation and homothety, and introduce interesting, meaningful and visual models for teaching of a plane transformation geomeoy which are obtained by using Mathematica. Moreover, this study will show how to visualize linear transformation for student's better understanding in teaching a plane transformation geometry in classroom. New development of these kinds of teaching-learning methods can simulate student's curiosity about mathematics and their interest. Therefore these models will give teachers the active teaching and also give students the successful loaming for obtaining the concept of linear transformation.

• Journal of Institute of Control, Robotics and Systems
• /
• v.7 no.7
• /
• pp.622-631
• /
• 2001

This paper presents a fuzzy modified PID controller that uses linear fuzzy inference method. In this structure, the proportional and derivative gains vary with the output of the system under control. 2-input PD type fuzzy controller is designed to obtain the varying gains. The proposed fuzzy PID structure maintains the same performance as the same performance as the general-purpose linear PID controller, and enhances the tracking performance over a wide range of input. Numerical simulations and experimental results show the effectiveness of the fuzzy PID controller in comparison with the conventional PID controller.

• Journal of Power System Engineering
• /
• v.10 no.4
• /
• pp.159-164
• /
• 2006

In recent, the marine engine of a large size is being realized a lower speed, longer stroke and a small number of cylinders for the energy saving. Consequently the variation of rotational torque became larger than former days because of the longer delay-time in fuel oil injection process and an increased output per cylinder. It was necessary that algorithms have enough robustness to suppress the variation of the delay-time and the parameter perturbation. This paper shows the structure of hybrid F-NFC against the delay-time and the perturbation of engine parameter as modeling uncertainties, and the design of the robust speed controller by hybrid F-NFC for the engine. And, The Parameter values of linear equation are determined by RC-GA for F-NFS. The hybrid F-NFC is combined the F-NFC and PID controller for filling up each.