• Journal of the Korean School Mathematics Society
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• v.16 no.3
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• pp.499-518
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• 2013

The purpose of this study is to examine the preservice secondary mathematics teachers understanding and dimensions of knowledge about definition of irrational numbers and irrational numbers and operations. I adopted a framework consisting of formal dimensions, intuitive numbers, algorithmic dimentions suggested by Tirosh et al.(1998) by adding instrumental dimension for his study. I surveyed 65 preservice secondary mathematics teachers who are in bachelor program and post-bachelor program for teacher certificate by using a questionnaire suggested by Sirotic and Zazkis(2007). The results of this study suggest that 83.1% of the participants gave correct answers in definitions of irrational numbers. 43% of the preservice secondary teachers gave correct answers in adding with irrational numbers. Also 91% of the preservice teachers gave correct answers in multiplying irrational numbers. The preservice teachers appeared to understand irrational numbers and operations at formal dimension. More than half of the preservice teachers gave incorrect answers in adding irrational numbers and a few participants gave incorrect in multiplying irrational numbers. The preservice teachers seemed to understand irrational numbers and operations at intuitive or instrumental dimension. The results also suggest that the preservice secondary mathematics teachers have incorrect understanding about irrational numbers.

• International Journal of Fuzzy Logic and Intelligent Systems
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• v.7 no.1
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• pp.85-89
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• 2007

Many authors considered the computational aspect of sup-min convolution when applied to weighted average operations. They used a computational algorithm based on a-cut representation of fuzzy sets, nonlinear programming implementation of the extension principle, and interval analysis. It is well known that $T_W$(the weakest t-norm)-based addition and multiplication preserve the shape of L-R type fuzzy numbers. In this paper, we consider the computational aspect of the extension principle by the use of $T_W$ when the principle is applied to fuzzy weighted average operations. We give the exact solution for the case where variables and coefficients are L-L fuzzy numbers without programming or the aid of computer resources.

• Journal of the Korean Data and Information Science Society
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• v.13 no.2
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• pp.209-216
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• 2002

In this paper, we introduce a concept of (H)-property which generalize that of increasing(decreasing) property of binary operation. We also treat some works related to operations on fuzzy numbers and generalize earlier results of Kawaguchi and Da-te(1994).

• Proceedings of the Korean Operations and Management Science Society Conference
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• 1996.04a
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• pp.76-78
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• 1996

When data is classified and each class has weight, the mean of data is a weighted average. When the class values and weights are trapezoidal fuzzy numbers, we can prove the weghted average is a fuzzy number though not trapezoidal. Its 4 corner points are obtained.

• The Mathematical Education
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• v.50 no.1
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• pp.41-59
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• 2011

Given the importance of algebra in the early grades, this paper analyzed the contents of whole numbers and their operations from the perspectives of generalized arithmetic. In particular, the focus of analysis was given to the properties of 0 and 1, those of operations such as commutativity, associativity, and distributivity, and the relations between operations. As such, this paper analyzed in detail how such properties and relations were introduced and expanded across different grades. It is expected that many issues in this paper will serve basic information to develop instructional materials in a way to fostering students' algebraic thinking in the elementary grades.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2000.11a
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• pp.53-56
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• 2000

In this paper, we define a concept of some set-theoretical operations of L-R type fuzzy numbers and discuss some properties of these concepts. Using these results, we discuss a concept of cardinality of type-two fuzzy sets.

• Communications for Statistical Applications and Methods
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• v.7 no.3
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• pp.643-654
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• 2000

In this paper, we review some class of t-norms on which fuzzy arithmetic operations preserve the shapes of fuzzy numbers and the Hausdorff-distance between fuzzy numbers as the measure of distance between fuzzy numbers. And we suggest the least Hausdorff-distance square method for fuzzy linear regression model using shape preserving fuzzy arithmetic operations.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.2
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• pp.253-266
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• 2011

We would like to generalize about trapezoidal fuzzy set and to calculate four operations based on the Zadeh's extension principle for two generalized trapezoidal fuzzy sets. And we roll up triangular fuzzy numbers and generalized triangular fuzzy sets into it. Since triangular fuzzy numbers and generalized triangular fuzzy sets are generalized trapezoidal fuzzy sets, we need no more the separate painstaking calculations of addition, subtraction, multiplication and division for two such kinds once the operations are done for generalized trapezoidal fuzzy sets.

• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.513-520
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• 2005

We calculate the normal fuzzy probability for trigonometric fuzzy numbers defined by trigonometric functions. And we study the normal probability for some operations of two trigonometric fuzzy numbers. Furthermore, we calculate the normal fuzzy probability for some fuzzy numbers generated by operations.

• Proceedings of the Korean Institute of Intelligent Systems Conference
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• 2002.12a
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• pp.22-24
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• 2002

Computation with fuzzy numbers is a prospective branch of a fuzzy set theory regarding the data processing applications. In this paper we consider an open problem about distributivity of fuzzy Quantities based on the extension principle suggested by Mares (1997). Indeed, we show that the distributivity on the class of fuzzy numbers holds and min-norm is the only continuous f-norm which holds the distributivity under f-norm based fuzzy arithmetic operations.