• 대한수학회지
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• 제60권5호
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• pp.931-957
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• 2023

For an arbitrary integer x, an integer of the form $$T(x)={\frac{x^2+x}{2}}$$ is called a triangular number. Let α₁, ... , α_k be positive integers. A sum ${\Delta}_{{\alpha}_1,{\ldots},{\alpha}_k}(x_1,\,{\ldots},\,x_k)=\{\alpha}_1T(x_1)+\,{\cdots}\,+{\alpha}_kT(x_k)$ of triangular numbers is said to be almost universal with one exception if the Diophantine equation ${\Delta}_{{\alpha}_1,{\ldots},{\alpha}_k}(x_1,\,{\ldots},\,x_k)=n$ has an integer solution (x₁, ... , x_k) ∊ ℤ^k for any nonnegative integer n except a single one. In this article, we classify all almost universal sums of triangular numbers with one exception. Furthermore, we provide an effective criterion on almost universality with one exception of an arbitrary sum of triangular numbers, which is a generalization of "15-theorem" of Conway, Miller, and Schneeberger.

• 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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• 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.

• 대한수학회보
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• 제58권3호
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• pp.603-608
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• 2021

Fix k ≥ 3. If a multiplicative function f satisfies f(x₁ + x₂ + ⋯ + x_k) = f(x₁) + f(x₂) + ⋯ + f(x_k) for arbitrary positive triangular numbers x₁, x₂, …, x_k, then f is the identity function. This extends Chung and Phong's work for k = 2.

• Advances in Computational Design
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• 제2권1호
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• pp.29-42
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• 2017

This study presents algorithms for determining the fuzzy critical loads of planar steel frame structures with fixity factors of beam - column and column - base connections are modeled as triangular fuzzy numbers. The finite element method with linear elastic semi-rigid connection and Response Surface Method (RSM) in mathematical statistic are applied for problems with symmetric triangular fuzzy numbers. The ${\alpha}$ - level optimization using the Differential Evolution (DE) involving integrated finite element modeling is proposed to apply for problems with any triangular fuzzy numbers. The advantage of the proposed methodologies is demonstrated through some example problems relating to for the twenty - story, four - bay planar steel frames.

• 대한수학회보
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• 제36권2호
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• pp.273-285
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• 1999

In this paper we establish the weak law of large numbers for randomly weighted partial sums of random variables and study conditions imposed on the triangular array of random weights {$W_{nj}{\;}:{\;}1{\leq}j{\leq}n,{\;}n{\geq}1$} and on the triangular array of random variables {$X_{nj}{\;}:{\;}1{\leq}j{\leq}n,{\;}{\geq}1$} which ensure that $\sum_{j=1}^{n}{\;}W_{nj}{\mid}X_{nj}{\;}-{\;}B_{nj}{\mid}$ converges In probability to 0, where {$B_{nj}{\;}:{\;}1{\;}{\leq}{\;}j{\;}{\leq}{\;}n,{\;}n{\;}{\geq}{\;}1$} is a centering array of constants or random variables.

• 태양에너지
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• 제9권1호
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• pp.43-52
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• 1989

Heat transfer rate and heat flux from the condenser with internally triangular fins rotating heat pipe has been numerically studied by finite element method. The results of numerical and P.J. Martos' experimental showed good agreement and it was able to predict to the performance of a rotating heat pipe. By increasing fin half angle or fin height, heat transfer rate from condenser was increased slightly but heat flux was decreased. By increasing condenser radius or r.p.m. of rotating heat pipe, heat transfer rate and heat flux was increased rapidly. Heat transfer rate was rapidly increased with increasing fin numbers in case of few fm numbers but slowly increased at many fin numbers. So the optimum fin numbers were a half of maximum fin numbers which was able to install in the condenser of a rotating heat pipe.

• 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.

• Journal of applied mathematics & informatics
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• 제41권2호
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• pp.311-320
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• 2023

In this article, a new penalty and different ranking algorithms are used to find the lowest transportation costs for the fuzzy transportation problem. This approach utilises different ranking techniques when dealing with triangular fuzzy numbers. Also, we find that the fuzzy transportation solution of the proposed method is the same as the Fuzzy Modified Distribution Method (FMODI) solution. Finally, examples are used to show how a problem is solved.