A Fuzzy Numerical Simulation-based Heuristic Method for Fully Fuzzy Systems of Linear Equations

Hande Günay Akdemir

doi:10.31466/kfbd.1275692

TR EN

Tam Bulanık Lineer Denklem Sistemleri için Bulanık Sayısal Simülasyon Tabanlı Sezgisel Bir Yöntem

Abstract

Bu çalışmada, tam bulanık lineer denklem sistemlerine yaklaşık çözümler bulmak için yeni bir yöntem önerilmiştir. Teknik, bir ikiye bölme yöntemini bulanık sayısal simülasyon ile bütünleştirir. Prosedür, bulanık parametrelerin tek değerlerinin üretilmesi ve çözümlerin alt ve üst sınırlarının belirlenmesi için ortaya çıkan net problemlerin tekrar tekrar çözülmesiyle başlar. Ortalama alt ve üst sınır değerleri hesaplandıktan sonra, elde edilen supremum ve infimum değerler sırasıyla çözümlerin alt ve üst sınırları olarak kabul edilir. Eşitliklerin sağ ve sol taraflarının karşılık gelen alt ve üst sınırları arasındaki mutlak farkların toplamına ilişkin bir hata fonksiyonu ele alınarak çözümler geliştirilmeye çalışılmıştır. Çözümler için çok büyük aralıklar elde edildiğinde, hata değerini azaltmak için ikiye bölme algoritması uygulanır. Yöntem, daha gerçekçi olmak için değişkenlerin ve/veya katsayıların negatif olmayan sınırlamalarını kaldırarak keyfi bulanık sayılar için büyük boyutlu kare sistemleri çözmeyi amaçlar. Hesaplama yöntemi kapsamlı bir şekilde sunulduktan sonra, son olarak bazı kıyaslama örnekleri verilmektedir.

Keywords

Yaklaşık çözüm, İkiye bölme yöntemi, Tam bulanık lineer denklem sistemleri, Bulanık sayısal simülasyon

A Fuzzy Numerical Simulation-based Heuristic Method for Fully Fuzzy Systems of Linear Equations

Abstract

In this paper, a new method is proposed to find the approximate solutions to fully fuzzy systems of linear equations (FFSLEs). The technique integrates a bisection method with Fuzzy Numerical Simulation (FNS). The procedure starts with generating single values of fuzzy parameters and solving the resulting crisp problems repeatedly to determine the lower and upper bounds of the solutions. After computing the mean lower and upper bound values, the obtained supremum and infimum values are considered to be the lower and upper bounds of the solutions, respectively. It is attempted to improve solutions by considering an error function related to the sum of the absolute differences between the corresponding lower and upper bounds of the left and right sides of the equalities. When very large intervals are obtained for the solutions, the bisection algorithm is applied to reduce the error value. The method intends to solve square systems of large dimensions for arbitrary fuzzy numbers (FNs) by removing non-negativity confinements of the variables and/or coefficients to be more realistic. After the computational method is presented thoroughly, some benchmark examples are finally provided.

Keywords

Approximate solution, Bisection method, Fully fuzzy systems of linear equations, Fuzzy numerical simulation

References

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Details

Primary Language

English

Subjects

Mathematical Sciences

Journal Section

Research Article

Authors

Hande Günay Akdemir ^*
0000-0003-3241-1560
Türkiye

Early Pub Date

December 18, 2023

Publication Date

December 15, 2023

Submission Date

April 2, 2023

Acceptance Date

November 11, 2023

Published in Issue

Year 2023 Volume: 13 Number: 4

DOI

https://doi.org/10.31466/kfbd.1275692

IZ

https://izlik.org/JA36HA48CK

APA

Günay Akdemir, H. (2023). A Fuzzy Numerical Simulation-based Heuristic Method for Fully Fuzzy Systems of Linear Equations. Karadeniz Fen Bilimleri Dergisi, 13(4), 1361-1376. https://doi.org/10.31466/kfbd.1275692

AMA

1.Günay Akdemir H. A Fuzzy Numerical Simulation-based Heuristic Method for Fully Fuzzy Systems of Linear Equations. KFBD. 2023;13(4):1361-1376. doi:10.31466/kfbd.1275692

Chicago

Günay Akdemir, Hande. 2023. “A Fuzzy Numerical Simulation-Based Heuristic Method for Fully Fuzzy Systems of Linear Equations”. Karadeniz Fen Bilimleri Dergisi 13 (4): 1361-76. https://doi.org/10.31466/kfbd.1275692.

EndNote

Günay Akdemir H (December 1, 2023) A Fuzzy Numerical Simulation-based Heuristic Method for Fully Fuzzy Systems of Linear Equations. Karadeniz Fen Bilimleri Dergisi 13 4 1361–1376.

IEEE

[1]H. Günay Akdemir, “A Fuzzy Numerical Simulation-based Heuristic Method for Fully Fuzzy Systems of Linear Equations”, KFBD, vol. 13, no. 4, pp. 1361–1376, Dec. 2023, doi: 10.31466/kfbd.1275692.

ISNAD

Günay Akdemir, Hande. “A Fuzzy Numerical Simulation-Based Heuristic Method for Fully Fuzzy Systems of Linear Equations”. Karadeniz Fen Bilimleri Dergisi 13/4 (December 1, 2023): 1361-1376. https://doi.org/10.31466/kfbd.1275692.

JAMA

1.Günay Akdemir H. A Fuzzy Numerical Simulation-based Heuristic Method for Fully Fuzzy Systems of Linear Equations. KFBD. 2023;13:1361–1376.

MLA

Günay Akdemir, Hande. “A Fuzzy Numerical Simulation-Based Heuristic Method for Fully Fuzzy Systems of Linear Equations”. Karadeniz Fen Bilimleri Dergisi, vol. 13, no. 4, Dec. 2023, pp. 1361-76, doi:10.31466/kfbd.1275692.

Vancouver

1.Hande Günay Akdemir. A Fuzzy Numerical Simulation-based Heuristic Method for Fully Fuzzy Systems of Linear Equations. KFBD. 2023 Dec. 1;13(4):1361-76. doi:10.31466/kfbd.1275692

The published articles in The Black Sea Journal of Sciences are licensed under Creative Commons Attribution-NonCommercial 4.0 International

Tam Bulanık Lineer Denklem Sistemleri için Bulanık Sayısal Simülasyon Tabanlı Sezgisel Bir Yöntem

Abstract

Keywords

A Fuzzy Numerical Simulation-based Heuristic Method for Fully Fuzzy Systems of Linear Equations

Abstract

Keywords

References

Details

Primary Language

Subjects

Journal Section

Authors

Early Pub Date

Publication Date

Submission Date

Acceptance Date

Published in Issue

DOI

IZ

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