ON QUOTIENT DIFFERENCE ALGEBRAS VIA FUZZY IDEALS

Roh, Eun-Hwan 진주교육대학교 과학교육연구소 2000 科學敎育硏究 Vol.26 No.-

1914년 Hallsdorff는 poset과 군을 결합하여 새로운 대수 구조인 순서군(ordered group)을 만들었다. Meng은 1992년 Hausdorff의 아이디어를 poset과 BCK-대수에 응용하여 difference 대수로 명명하고 difference 대수는 순서군, BCK-대수 그리고 BCI-대수의 일반화이고 가환군과 동치가될 필요충분조건을 증명하였다. 그러나 그동안 difference 대수는 수학자들의 주목을 받지 못하였다. 그 이유 중 하나는 difference 대수의 공리가 서로 독립적이라는 예를 찾을 수 없었기 때문이었다. 최근 Roh등은 difference 대수의 공리가 서로 독립적이라는 것를 보이고([RJKS1])이 분야에 대해 활발한 연구를 하고 있다. 한편, 1965년 Zadeh교수는 퍼지집합을 소개하였고 퍼지집합은 공학, 의학, 화학, 수학 등에 적용되어 왔으며, 근래에는 생활과 직접적인 연관을 갖는 형태로 그 응용력을 보여주고 있다. 본 연구에서는 difference대수에 퍼지 개념을 접목시켜 다음의 결과를 얻었다. 첫째, 퍼지 아이디얼을 이용하여 상(quotient) difference 대수를 만들었다. 둘째, 퍼지 준동형 기본 정리를 증명하고 이 결과를 이용하여 준동형 기본 정리와 제 1 동형 정리를 얻었다. We introduce the concept of a fuzzy ideal in a difference algebra X. Next, we give a construction of a quotient difference algebra X/μ by a fuzzy ideal μ in X and the fuzzy homomorphism fundamental theorem.

정의적 특성이 수학적 문제 해결력에 미치는 영향

강호욱,노은환,박은진,송현준,이혜경,주채연 진주교육대학교 초등교육연구소 2005 科學敎育硏究 Vol.28 No.-

The purpose of this study is to provide some basic data which can be helpful for improving the methods of mathematics teaching-learning emphasizing the affective factors by investigating the effect on affective characteristics and mathematical problem solving ability of the students on the elementary school sixth grade. In order to achieve these purpose, the following research problems were set up for the present study: The results of this study are as follows: First, it was appeared that there was not any difference on attitude on mathematics, belief, self-confidence and the degree of mathematical problem solving ability by sex. Second, it was appeared that there was some statistical meaningful difference on attitude on mathematics, belief, self-confidence and the degree of mathematical problem solving ability according to high middle low ability on mathematics which the students think that they have. Based on the results of this study, I'd like to give some suggestions as followings to provide some help to teaching and learning mathematics. First, the succeeding studies are needed by selecting different population from the population of this study, classifying low-ranking factors consisting of affective characteristics differently from this study, compounding each low-ranking factors in various manners like using new items, etc. Second, the succeeding studies are needed in this part, because what mathematical belief teachers have mathematics can have an effect on students' mathematical belief and action as well as on teachers' thinking process and action in the class. Third, the succeeding studies are needed to develop concrete field study and program which can be helpful for improving actually students' affective behavior characteristics in school field.

초등학생의 성격유형과 수학적 성향의 관계

김정혜,노은환 晋州敎育大學校 科學敎育硏究院 2006 科學敎育硏究 Vol.29 No.-

MMTIC (Murphy-Meisgeir Type Indicator for Children), which is a tool to measure the inborn psychological functions of children and adolescents, was developed based on Jung's theory of psychological patterns for the use by children and adolescents in their everyday life. We can use the tool to understand differences in personality type among people and to achieve educational goals in the field of education. The purposes of the present study were to survey the distribution of personality type of elementary students in the Sancheong -gun area, which is exposed to natural environment relatively much, to examine the relation between their personality type and their mathematical disposition, and to understand differences in personality type of people and use them for teaching- learning, adjustment to school life, counseling, etc. in the field of education. For these purposes, we formulated research questions as follows. 1. How is the distribution of personality type of elementary students in the Sancheong-gun area? 2. In the personality type of elementary students in the Sancheong-gun area related to their mathematical disposition? 2-1. How are the four preference indexes of personality type related to mathematical disposition? 2-2. How are the four psychological functions of personality type related to mathematical disposition? 2-3. How are the four temperaments of personality type related to mathematical disposition? In order to answer these questions, we surveyed 207 sixth-grade students in six elementary schools in Sancheong-gun, Personality type was tested MMTIC. and mathematical disposition was measured with a test composed of 22 questions, which was developed by the author and the reliability of which was confirmed through a preliminary test. Each question in the mathematical disposition test was on a scale of 4 points. A high score meant high mathematical disposition. MMTIC was analyzed by a special institution, and data for examining the relation between personality type and mathematical disposition were processed using SPSS 10.0. In order to examine the distribution of children's personality type by preference index, by psychological function and by temperament, we calculated frequencies and percentages. In addition, t-test was made to determine the significance of the relation between the preference indexes of personality type and mathematical disposition, and F-test was made to determine the significance of the relations between the psychological functions of personality type and mathematical disposition, and F-test was made to determine the significance of the relations between the psychological functions of personality type and mathematical disposition and between the temperaments of personality type and mathematical disposition. From the results of this study were drawn conclusions as follows. First, when children were compared based on preference indexes, a significantly larger number of students were external(E) in the external-internal(EI) index, intuition(N) in the sensing- intuition(SN) index. feeling(F) in thinking-feeling(TF) index, and perceptive in judging-perceiving(JP) index. In the distribution of psychological functions, intuition- feeling(NF) children were most frequent and, next, sensing-feeling (SF), intuition-thinking(NT) and sensing-thinking(ST) children. In the distribution of temperament, the percentage of children with intuition-feeling(NF) temperament was highest and it was particularly as high as 15.9% among male students and, next, the percentages of children with sensing-perception(SP), sensing-judging(SJ) and intuition-thinking(NT) temperaments in their order. Second, in order to examine the relation of mathematical disposition with the preference indexes(EI, SN, TF, JP) and the psychological functions(ST, SF, NT, NF) of personalty type, we conducted t-test and F-test. According to the results, no statistically significant difference was observed at significance level of 0.05 although there were slight differences of the means in all of the four types. Third, in order to examine the relation between mathematical disposition and the four temperaments (SP, SJ, NT, NF) of personal type, we conducted F-test. According to the results, statistically significant differences were observed at significance level of 0.05 and mathematical disposition was high in order of NT>NF>SJ>SP. Data collected through this research can be a guideline for establishing education plans for elementary students in Sancheong-gun. That is , because there are relatively many students with external disposition in the EI index, education may be focused more on activities. Because there are more students with emotional disposition in the TF index, small- group learning may be emphasized more than individual learning. With regard to the JP index, because most students have perceptive disposition, the tendency may be considered in teaching for higher educational effects. People who prefer the perceptive type generally want to adjust themselves to situations and to live with our restriction, tend to make efforts to understand life rather than control life, adjust themselves at a moment, and like to be openhearted. In addition, as they are fond of various opportunities, they can adapt themselves well to unorganized and uncertain situations. Moreover, they often fail to complete works and to be late in task performance. What is more, whenever such things happen, they usually cope with the situations appropriately by themselves. Understanding students' personality type does not necessarily mean better education. However, it is also absurd to establish education plans and give classes without knowing their characteristics. On the whole, research must begin with the identification of students' unique characteristics so that students' potential for future development can be acknowledged and their development can be promoted properly. Because students' mathematical disposition has a significant effect on their achievement in mathematics, this research began with the identification of students' personality type and explored the relation between students' personality type and their mathematical disposition. Researches should be continued on personality type and various factors affecting students' academic achievements. Such researches will enable customized education.

ON ANTI FUZZY TRANSLATION BH-IDEALS IN BH-ALGEBRAS

ROH, EUN HWAN 晋州敎育大學校 科學敎育硏究所 1999 科學敎育硏究 Vol.25 No.-

1966년 일본인 수학자 Imai교수와 Iseki교수는 새로운 대수적 구조인 BCK-대수를 소개하였고, 같은 해에 Iseki교수는 BCK-대수를 일반화 한 BCI-대수를 만들어 발표하였다. 1965년 Zadeh교수는 퍼지집합을 소개하였고 퍼지집합은 공학, 의학, 화학, 수학 등에 적용되어 왔으며, 근래에는 우리 생활과 직접적인 연관을 가지는 대단한 응용력을 보여주고 있다. 그동안 BCK?BCI-대수는 여러가지 형태로 연구되어 왔으며 특히 아이디얼이론과 필터이론은 이 분야의 연구에서 아주 중요한 역활을 한다. 한편, ground field의 확장은 대단히 어려운 문제이지만 의미있는 일인데 1998년 Jun, Roh 그리고 Kim교수는 BCK?BCI-대수를 일반화한 BH-대수를 소개하고 여러가지 성질들을 얻었다. 본 연구에서는 BH-대수에 퍼지 개념을 접목시켜 BH-대수에서의 여러가지 퍼지 아이디얼의 성질을 연구하고자한다. We consider the fuzzification of (translation) BH-ideals in BH-algebras, and investigate some related properties.

On prime dual ideals in BCK-algebras

Roh, Eun-Hwan,Jun, Young-Bae,Huang, Yi-Sheng Korean Mathematical Society 1995 대한수학회논문집 Vol.10 No.3

In [1], Ahmad has given a characterization of prime dual ideals in bounded commutative BCK-algebras. The aime of this paper is to show that Theorem of [1] holds without the commutativity.

On Prime Dual Ideals in BCK-algebras II

Roh, Eun-Hwan ...et al KYUNGPOOK UNIVERSITY 1998 Kyungpook mathematical journal Vol.38 No.2

In [3], Ahmad has given a characterization of prime dual ideal, principal prime ideal and ∨-irreducible dual ideal in bounded commutative BCK-algebras. The aim of this paper is to show that Theorem of [3] holds without the commutativity. Finally we show that there is a prime dual ideal in an upper semilattice BCK-algebras.

On Difference Algebras

Eun Hwan Roh,Seon Yu Kim,Young Bae Jun,Wook Hwan Shim 경북대학교 자연과학대학 수학과 2003 Kyungpook mathematical journal Vol.43 No.3

In this paper, we introduce the concept of the quotient difference algebra via an ideal and investigate some related properties.

DIRECT SUM ON WFI-ALGEBRAS

Eun Hwan Roh 충청수학회 2009 충청수학회지 Vol.22 No.3

The notion of subdirect sum and direct sum in WFI-algebras is introduced, and several properties are investigated.

PRIME IDEALS IN SUBTRACTION ALGEBRAS

ROH, EUN HWAN 호남수학회 2006 호남수학학술지 Vol.28 No.3

Prime elements and ${\bigwedge}$-irreducible elements are introduced, and related properties are investigated.

A NOTE ON COMPLICATED SUBTRACTION ALGEBRAS

Roh, Eun-Hwan The Honam Mathematical Society 2007 호남수학학술지 Vol.29 No.3

We provided characterizations of complicated in a subtraction algebra, and we showed that the complicated subtraction algebra is a ring.