• Journal of Intelligence and Information Systems
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• v.12 no.3
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• pp.15-32
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• 2006

The increasing complexity of the socio-economic environments makes it less and less possible for single decision-maker to consider all relevant aspects of problem. Therefore, many organizations employ groups in decision making. In this paper, we present a multiperson decision making method using fuzzy logic with linguistic quantifier when each of group members specifies imprecise judgments possibly both on performance evaluations of alternatives with respect to the multiple criteria and on the criteria. Inexact or vague preferences have appeared in the decision making literatures with a view to relaxing the burdens of preference specifications imposed to the decision-makers and thus taking into account the vagueness of human judgments. Allowing for the types of imprecise judgments in the model, however, makes more difficult a clear selection of alternative(s) that a group wants to make. So, further interactions with the decision-makers may proceed to the extent to compensate for the initial comforts of preference specifications. These interactions may not however guarantee the selection of the best alternative to implement. To circumvent this deadlock situation, we present a procedure for obtaining a satisfying solution by the use of linguistic quantifier guided aggregation which implies fuzzy majority. This is an approach to combine a prescriptive decision method via a mathematical programming and a well-established approximate solution method to aggregate multiple objects.

• The Journal of Art Theory & Practice
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• no.7
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• pp.165-188
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• 2009

In the development of linear perspective, Brook Taylor's theory has achieved a special position. With his method described in Linear Perspective(1715) and New Principles of Linear Perspective(1719), the subject of linear perspective became a generalized and abstract theory rather than a practical method for painters. He is known to be the first who used the term 'vanishing point'. Although a similar concept has been used form the early stage of Renaissance linear perspective, he developed a new method of British perspective technique of measure points based on the concept of 'vanishing points'. In the 15th and 16th century linear perspective, pictorial space is considered as independent space detached from the outer world. Albertian method of linear perspective is to construct a pavement on the picture in accordance with the centric point where the centric ray of the visual pyramid strikes the picture plane. Comparison to this traditional method, Taylor established the concent of a vanishing point (and a vanishing line), namely, the point (and the line) where a line (and a plane) through the eye point parallel to the considered line (and the plane) meets the picture plane. In the traditional situation like in Albertian method, the picture plane was assumed to be vertical and the center of the picture usually corresponded with the vanishing point. On the other hand, Taylor emphasized the role of vanishing points, and as a result, his method entered the domain of projective geometry rather than Euclidean geometry. For Taylor's theory was highly abstract and difficult to apply for the practitioners, there appeared many perspective treatises based on his theory in England since 1740s. Joshua Kirby's Dr. Brook Taylor's Method of Perspective Made Easy, Both in Theory and Practice(1754) was one of the most popular treatises among these posterior writings. As a well-known painter of the 18th century English society and perspective professor of the St. Martin's Lane Academy, Kirby tried to bridge the gap between the practice of the artists and the mathematical theory of Taylor. Trying to ease the common readers into Taylor's method, Kirby somehow abbreviated and even omitted several crucial parts of Taylor's ideas, especially concerning to the inverse problems of perspective projection. Taylor's theory and Kirby's handbook reveal us that the development of linear perspective in European society entered a transitional phase in the 18th century. In the European tradition, linear perspective means a representational system to indicated the three-dimensional nature of space and the image of objects on the two-dimensional surface, using the central projection method. However, Taylor and following scholars converted linear perspective as a complete mathematical and abstract theory. Such a development was also due to concern and interest of contemporary artists toward new visions of infinite space and kaleidoscopic phenomena of visual perception.

• Journal of Elementary Mathematics Education in Korea
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• v.20 no.3
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• pp.431-456
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• 2016

The purpose of this study is to investigate the appropriate time of introduction and the usage of the number line, in order to suggest the right point of learning the number concept to the elementary school students. For the efficient achievement of this purpose, we investigated the mathematical models for constructing the number concept such as number line, empty number line and double number line, counting and development of number concept. Then, we conducted case study on the time of introduction and the usage of the number line. Finally, we analyzed the result. First, there is need for adjustment to conduct the introduction of the number line from the second year of elementary school, so to help the students understand the continuing number concept through the understanding on the metaphorical concept of the number line. Second, there is the need of positive introduction and the use on the mathematical models; empty number line which helps to draw various thinking strategy visually through the process of operations such as addition and subtraction; the division into equal part and division by equal part in which multiplicative comparative situation or division takes place; the double number line which helps to understand the rate or proportional distribution. Finally, when adopting the number line, the empty number line, or the double number line, we suggested the necessity of learning about elaborate guidance and the usage in order to fully understand the metaphorical concept of the number line.

• School Mathematics
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• v.15 no.3
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• pp.603-617
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• 2013

The major purpose of this article is to examine what kind of gap exists between mathematically gifted students' probability knowledge and the reality actually applying that knowledge and then analyze the cause of the gap. To attain the goal, 23 elementary mathematically gifted students at the highest level from G region were provided with problem situations internalizing a probability and expectation, and the problems are in series in which conditions change one by one. The study task is in a gaming situation where there can be the most reasonable answer mathematically, but the choice may differ by how much they consider a certain condition. To collect data, the students' individual worksheets are collected, and all the class procedures are recorded with a camcorder, and the researcher writes a class observation report. The biggest reason why the students do not make a decision solely based on their own mathematical knowledge is because of 'impracticality', one of the properties of probability, that in reality, all things are not realized according to the mathematical calculation and are impossible to be anticipated and also their own psychological disposition to 'avoid loss' about their entry fee paid. In order to provide desirable probability education, we should not be limited to having learners master probability knowledge included in the textbook by solving the problems based on algorithmic knowledge but provide them with plenty of experience to apply probabilistic inference with which they should make their own choice in diverse situations having context.

• Communications of Mathematical Education
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• v.23 no.3
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• pp.643-682
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• 2009

There is no doubt that the national competitiveness, in 21st century, definitely depends on how effectively it has been producing high-qualify human resources. It is inevitable that we are required to produce outstanding people who are going to make the use of highly developed scientific technology. Every country has already set to concentrate their all efforts in cultivating competitive human resources, enabling it to strengthen its national competitiveness. We Korea, in order to keep up with it, have arranged legal and systematic basis and are putting spurs to producing competent human resources under the 영재교육진흥법 및 시행령, which took effect from March, 2002. With the lack of experience and short history of Gifted Education, however, it is true that we still have many problems in promoting it in reality, We are asked to improve it by finding out what problems we have in whole area of Gifted Education, such as defining conception, choosing target students, structuring system and managing students afterwards. Therefore, this study, especially focusing on Math of Gifted Education is to investigate the present situation of Gifted Education and to examine what we should do for administering Gifted Education in effective ways.

• The Mathematical Education
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• v.61 no.3
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• pp.419-439
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• 2022

This study is based on Freudenthal's mathmatising process and the didactical phenomenology of linear function concept, I have described and examined the process in which students represent the constant rate of change into tables, graphs and equations and, in this way, how they construct mental objects and essence of the linear function concept. The students used the proportionality as composite units, when they represented the phenomenon with constant rate of change into tables. When representing in graphs, all but one student represented it into a line. There were differences among the students in the level they were using the given conditions, co-variation perspective, and corresponding rules when formulating equations. The students compared the relationship between two variables in a multiplicative way, and under the guidance of teachers they reached to the understanding that its relationship becomes a constant. Moreover, they could construct mental objects of a constant rate of change, understanding the situation where the relationship between time difference and distance difference becomes one value, namely speed. The students had difficulties in connecting the rate of change with the inclination of a line. The students constructed the essence (concept) of linear functions, after building and organizing the image that the rate of change is constant, the graph is linear, and the equation is formulated as y=ax+b (a: inclination, b: intercept).

• The Journal of Korean Institute of Communications and Information Sciences
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• v.38B no.2
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• pp.97-104
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• 2013

This paper introduces waiting time based periodic packet discard policy for frame based scheduler. This policy can be used with conventional packet discard policy or buffer management schemes, such as drop-tail or random early detection. Proposed discard policy discards packets, which are stayed in the buffer longer than threshold, at every period of scheduling. This decision of discard is based on waiting time of packet. In this paper, mathematical analysis is performed with situation of network congestion. Also, the simulation is performed to evaluate the performance of proposed discard policy. In the result, proposed discard policy can limit queuing delay by threshold. Also, if the packet discard is performed before scheduling and threshold is set with smaller value than frame length, it can limit the throughput of traffic.

• Journal of the Korean Institute of Telematics and Electronics
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• v.11 no.4
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• pp.23-28
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• 1974

One of the consistent nuisances in accurate design of circuits containing coils with core is how to take into account the frequency dependence of Q of actual coils. The conventional equivalent circuit consisting of an inductance and a series (constant) resistance and possibly a parallel (constant) capacitance is of little use in this situation since the core loss itself is strongly dependent on the frequency. In order to circumvent this difficulty, in this paper, a mathematical expression for Q of a given core as a function of inductance and frequency is first assumed and parameters in this expression are optimiged so as to best fit the data provided by the core manufacturer or obtained experimentally. This expression is then utilized in accurate calculation of the frequency response of a given circuit required in the optimal design of circuits containing coils. In other words the proposed approach is an effective combination of an approximate expression of coil's Q and circuit optimisation technique, which seems to have solved, to a great extent, the stated difficulty associated with actual coils. As for the optimization technique, ths Fletcher-Powell procedure was employed and one example was given to illustrate the proposed approach.

• Journal of the Korean Institute of Intelligent Systems
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• v.11 no.4
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• pp.359-365
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• 2001

In this paper, we propose the design methodology of target tracking system using fuzzy basis function expansion(FBFE) based on virus evolutionary genetic algorithm (VEGA). In general, the objective of target tracking is to estimate the future trajectory of the target based on the past position of the target obtained from the sensor. In the conventional and mathematical nonlinear filtering method such as extended Kalman filter(EKF), the performance of the system may be deteriorated in highly nonlinear situation. To resolve these problems of nonlinear filtering technique, by appling artificial intelligent technique to the tracking control of moving targets, we combine the advantages of both traditional and intelligent control technique. In the proposed method, after composing training datum from the parameters of extended Kalman filter, by combining FDFE, which has the strong ability for the approximation, with VEGA, which prevent GA from converging prematurely in the case of lack of genetic diversity of population, and by idenLifying the parameters and rule numbers of fuzzy basis function simultaneously, we can reduce the tracking error of EKF. Finally, the proposed method is applied to three dimensional tracking problem, and the simulation results shows that the tracking performance is improved by the proposed method.

• Journal of The Korean Association For Science Education
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• v.34 no.3
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• pp.295-301
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• 2014

The purpose of this study is to investigate the difficulties of teachers and students on the unit about 'measuring weight.' In this research, we have acquired data about teachers through survey, interview, and self-reflection journals, at the same time we have collected information on the students through survey, assessment test, and interview. We have extracted the difficulties from analysis with constant comparison method. In addition, we have analysed the curriculum of science and mathematics to know the leaning sequence. The analysis had been checked up by experts in science education. The result of the study is as follows: The difficulties of teachers are from the lack of teachers' descriptive knowledge, disorder of conceptual hierarchy in the curriculum, poor experimental instruments, and low psychomotor skill of students. The difficulties of students are from common misconceptions, opaque concepts, lack of manipulation skill, insufficiency of mathematical ability, difficulty of application of principles to the real situation, and lack of problem-solving ability. In addition, teachers have recognized that students face more difficulties in experiment class, while students think that they face more difficulties in conceptual understanding class.