• 제목/요약/키워드: Triangular Fuzzy Numbers

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THE GENERALIZED TRAPEZOIDAL FUZZY SETS

  • Lee, BongJu;Yun, Yong Sik
    • 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.

2-차원 삼각퍼지수에 대한 Zadeh의 확장원리 (Zadeh's extension principle for 2-dimensional triangular fuzzy numbers)

  • 김창일;윤용식
    • 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.

Fuzzy analysis for stability of steel frame with fixity factor modeled as triangular fuzzy number

  • Tran, Thanh Viet;Vu, Quoc Anh;Le, Xuan Huynh
    • 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.

FUZZY TRANSPORTATION PROBLEM IS SOLVED UTILIZING SIMPLE ARITHMETIC OPERATIONS, ADVANCED CONCEPT, AND RANKING TECHNIQUES

  • V. SANGEETHA;K. THIRUSANGU;P. ELUMALAI
    • 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.

THE GENERALIZED TRIANGULAR FUZZY SETS

  • Yun, Yong Sik;Ryu, Sang Uk;Park, Jin Won
    • 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.

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Estimation of Parameters in Fuzzy Time Series Model with Triangular Fuzzy Numbers

  • 손은희;손건태
    • 한국통계학회:학술대회논문집
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    • 한국통계학회 2000년도 추계학술발표회 논문집
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    • pp.267-269
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    • 2000
  • Using the fuzzified coefficients, ARMA processes can be extended to fuzzy time series model. In this paper, the estimation of parameters in the fuzzy time series model with asymmetric triangular fuzzy coefficients is studied. Nonlinear programming is applied to get solutions of parameters.

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A Learning Algorithm of Fuzzy Neural Networks with Trapezoidal Fuzzy Weights

  • Lee, Kyu-Hee;Cho, Sung-Bae
    • 한국지능시스템학회:학술대회논문집
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    • 한국퍼지및지능시스템학회 1998년도 The Third Asian Fuzzy Systems Symposium
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    • pp.404-409
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    • 1998
  • In this paper, we propose a learning algorithm of fuzzy neural networks with trapezoidal fuzzy weights. This fuzzy neural networks can use fuzzy numbers as well as real numbers, and represent linguistic information better than standard neural networks. We construct trapezodal fuzzy weights by the composition of two triangles, and devise a learning algorithm using the two triangular membership functions, The results of computer simulations on numerical data show that the fuzzy neural networks have high fitting ability for target output.

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A STUDY OF TWO SPECIES MODEL WITH HOLLING TYPE RESPONSE FUNCTION USING TRIANGULAR FUZZY NUMBERS

  • P. VINOTHINI;K. KAVITHA
    • Journal of applied mathematics & informatics
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    • 제41권4호
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    • pp.723-739
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    • 2023
  • In this paper, we developed three theoretical models based on prey and predator that exhibit holling-type response functions. In both a fuzzy and a crisp environment, we have provided a mathematical formulation for the prey predator concept. We used the signed distance method to defuzzify the triangular fuzzy numbers using the alpha-cut function. We can identify equilibrium points for all three theoretical models using the defuzzification technique. Utilizing a variational matrix, stability is also performed with the two species model through three theoretical models. Results are presented, followed by discussion. MATLAB software is used to provide numerical simulations.

A CANONICAL REPRESENTATION FOR THE SOLUTION OF FUZZY LINEAR SYSTEM AND FUZZY LINEAR PROGRAMMING PROBLEM

  • NEHI HASSAN MISHMAST;MALEKI HAMID REZA;MASHINCHI MASHAALAH
    • Journal of applied mathematics & informatics
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    • 제20권1_2호
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    • pp.345-354
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    • 2006
  • In this paper first, we find a canonical symmetrical trapezoidal(triangular) for the solution of the fuzzy linear system $A\tilde{x}=\tilde{b}$, where the elements in A and $\tilde{b}$ are crisp and arbitrary fuzzy numbers, respectively. Then, a model for fuzzy linear programming problem with fuzzy variables (FLPFV), in which, the right hand side of constraints are arbitrary numbers, and coefficients of the objective function and constraint matrix are regarded as crisp numbers, is discussed. A numerical procedure for calculating a canonical symmetrical trapezoidal representation for the solution of fuzzy linear system and the optimal solution of FLPFV, (if there exist) is proposed. Several examples illustrate these ideas.