• 충청수학회지
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• 제26권2호
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• pp.297-308
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• 2013

We define one-sided quadrangular fuzzy sets, a left quadrangular fuzzy set and a right quadrangular fuzzy set. And then we generalize the results of addition, subtraction, multiplication, and division based on the Zadeh's extension principle for two one-sided quadrangular fuzzy sets. In addtion, we find the condition that the result of addition or subtraction for two one-sided quadrangular fuzzy sets becomes a triangular fuzzy number.

• 충청수학회지
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• 제27권2호
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• pp.277-286
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• 2014

We define the pentagonal fuzzy sets and generalize the results of addition, subtraction, multiplication, and division based on the Zadeh's extension principle for two pentagonal fuzzy sets. In addtion, we find the condition that the result of addition or subtraction for two pentagonal fuzzy sets becomes a triangular fuzzy number and give some example.

• 충청수학회지
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• 제24권2호
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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.

• 한국수학사학회지
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• 제33권5호
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• pp.277-287
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• 2020

There are many results for Zadeh's max-min composition operators based on Zadeh's extension principle. We calculate Zadeh's max-min composition operators for two triangular fuzzy numbers defined on ℝ.

• 한국지능시스템학회논문지
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• 제8권4호
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• pp.69-72
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• 1998

We introduce a concept of a 'fuzzy' map between sets by modifying the concetp of the extension principle introduced by Dubois and Prade in [1] and by using this we generalize Goguen's and Zadeh's extension principles in [2] and [3].

• 대한수학회논문집
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• 제28권3호
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• pp.635-642
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• 2013

There are many results on the extended operations of two fuzzy numbers based on the Zadeh's extension principle. For the calculation, we have to use existing operations between two ${\alpha}$-cuts. In this paper, we define parametric operations between two ${\alpha}$-cuts which are different from the existing operations. But we have the same results as the extended operations of Zadeh's principle.

• 한국지능시스템학회:학술대회논문집
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• 한국퍼지및지능시스템학회 1998년도 The Third Asian Fuzzy Systems Symposium
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• pp.376-379
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• 1998

We introduce the concept of a 'fuzzy' map between sets by modifying the concept of the extension principle introduced by Dubois and Prade in [1] and study their properties. Using these we generalize Goguen's and Zadeh's extension principles in [2] and [3].

• 한국지능시스템학회논문지
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• 제25권2호
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• pp.197-202
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• 2015

삼각퍼지수는 가장 유명한 퍼지수 중의 하나이다. 두 삼각퍼지수 사이의 확장된 대수적 작용소에 대한 많은 결과들이 알려져 있다. 우리는 $\mathbb{R}$ 위에 정의된 삼각퍼지수를 $\mathbb{R}^2$ 위로 일반화하였다. 영역을 값으로 갖는 두 ${\alpha}$-절단 사이에 매개변수 작용소를 정의함으로서 $\mathbb{R}^2$ 위에서 정의된 두 삼각퍼지수에 대한 매개변수 작용소를 얻을 수 있었다.

• 충청수학회지
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• 제22권2호
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• pp.161-170
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• 2009

For various fuzzy numbers, many operations have been calculated. We generalize about triangular fuzzy number and calculate four operations based on the Zadeh's extension principle, addition A(+)B, subtraction A(-)B, multiplication A(${\cdot}$)B and division A(/)B for two generalized triangular fuzzy sets.

• 한국데이터정보과학회:학술대회논문집
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• 한국데이터정보과학회 2006년도 추계 학술발표회 논문집
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• pp.81-95
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• 2006

The usual arithmetic operations on real numbers can be extended to arithmetical operations on fuzzy intervals by means of Zadeh's extension principle based on a t-norm T. A t-norm is called consistent with respect to a class of fuzzy intervals for some arithmetic operation if this arithmetic operation is closed for this class. It is important to know which t-norms are consistent with a particular type of fuzzy intervals. Recently Dombi and Gyorbiro proved that addition is closed if the Dombi t-norm is used with two bell-shaped fuzzy intervals. A result proved by Mesiar on a strict t-norm based shape preserving additions of LR-fuzzy intervals with unbounded support is recalled. As applications, we define a broader class of bell-shaped fuzzy intervals. Then we study t-norms which are consistent with these particular types of fuzzy intervals. Dombi and Gyorbiro's results are special cases of the results described in this paper.