Algebraic Modification of Trapezoidal Fuzzy Numbers to Complete Fully Fuzzy Linear Equations System Using Gauss-Jacobi Method

Ahmad Syaiful Abidin; Mashadi Mashadi; Sri Gemawati

doi:doi:10.11648/j.ijmfs.20190502.12

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Algebraic Modification of Trapezoidal Fuzzy Numbers to Complete Fully Fuzzy Linear Equations System Using Gauss-Jacobi Method

Ahmad Syaiful Abidin, Mashadi Mashadi, Sri Gemawati

Published in International Journal of Management and Fuzzy Systems (Volume 5, Issue 2)

Received: 20 July 2019 Accepted: 19 August 2019 Published: 2 September 2019

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Abstract

This paper will discuss algebraic modification of trapezoidal fuzzy numbers with a general form of fully fuzzy numbers is with is n × n fuzzy matrix, fuzzy vector, and unknown fuzzy vector. The concept used in this paper is define positive or negative fuzzy numbers determined by the area on the left side of the x-axis and the right side of the x-axis. Furthermore, the concept will be applied to the multiplication of two fully fuzzy trapezoidal numbers to produce a new algebra that can be applied to a system of linear equations. At the end, an example of multiplication two fully fuzzy trapezoidal numbers using the Gauss-Jacobi method will be given. As a result compatible number will be obtained.

Published in	International Journal of Management and Fuzzy Systems (Volume 5, Issue 2)
DOI	10.11648/j.ijmfs.20190502.12
Page(s)	40-46
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2019. Published by Science Publishing Group

Keywords

Fully Fuzzy Number, Trapezoidal, New Algebra, Gauss-Jacobi Method

References

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[4]	S. Gemawati, Nasﬁanti, Mashadi dan A Hadi, A new for dual fully fuzzy linear system with trapezoidal fuzzy number by QR decomposition, Journal of Physics, 1116, 2018, 1-5.
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[6]	A. Hadi, Mashadi dan S. Gemawati, On fuzzy n-inner product spaces, Journal of Physics, 020010, 2017, 1-6.
[7]	S. I. Marni, Mashadi, S. Gemawati, Solving dual fully fuzzy linear system by use factorizations of the coeficient matrix for trapezoidal fuzzy number, Bulletin of Mathematics, 2, 2018, 145-156.
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[9]	A. Kumar, Neetu, dan A. Bansal, A new method to solve fully fuzzy linear system with trapezoidal fuzzy number, Canadian Journal on Science and Engineering Mathematics, 1, 2010, 45-56.
[10]	A. Kumar, J. Kaur dan P singh, A new method for solving fuzzy linier programs with trapezoidal fuzzy numbers, Journal of Fuzzy, 2011, 2011, 1-12.
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APA Style

Ahmad Syaiful Abidin, Mashadi Mashadi, Sri Gemawati. (2019). Algebraic Modification of Trapezoidal Fuzzy Numbers to Complete Fully Fuzzy Linear Equations System Using Gauss-Jacobi Method. International Journal of Management and Fuzzy Systems, 5(2), 40-46. https://doi.org/10.11648/j.ijmfs.20190502.12

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ACS Style

Ahmad Syaiful Abidin; Mashadi Mashadi; Sri Gemawati. Algebraic Modification of Trapezoidal Fuzzy Numbers to Complete Fully Fuzzy Linear Equations System Using Gauss-Jacobi Method. Int. J. Manag. Fuzzy Syst. 2019, 5(2), 40-46. doi: 10.11648/j.ijmfs.20190502.12

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AMA Style

Ahmad Syaiful Abidin, Mashadi Mashadi, Sri Gemawati. Algebraic Modification of Trapezoidal Fuzzy Numbers to Complete Fully Fuzzy Linear Equations System Using Gauss-Jacobi Method. Int J Manag Fuzzy Syst. 2019;5(2):40-46. doi: 10.11648/j.ijmfs.20190502.12

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@article{10.11648/j.ijmfs.20190502.12,
  author = {Ahmad Syaiful Abidin and Mashadi Mashadi and Sri Gemawati},
  title = {Algebraic Modification of Trapezoidal Fuzzy Numbers to Complete Fully Fuzzy Linear Equations System Using Gauss-Jacobi Method},
  journal = {International Journal of Management and Fuzzy Systems},
  volume = {5},
  number = {2},
  pages = {40-46},
  doi = {10.11648/j.ijmfs.20190502.12},
  url = {https://doi.org/10.11648/j.ijmfs.20190502.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmfs.20190502.12},
  abstract = {This paper will discuss algebraic modification of trapezoidal fuzzy numbers with a general form of fully fuzzy numbers is  with  is n × n fuzzy matrix,  fuzzy vector, and  unknown fuzzy vector. The concept used in this paper is define positive or negative fuzzy numbers determined by the area on the left side of the x-axis and the right side of the x-axis. Furthermore, the concept will be applied to the multiplication of two fully fuzzy trapezoidal numbers to produce a new algebra that can be applied to a system of linear equations. At the end, an example of multiplication two fully fuzzy trapezoidal numbers using the Gauss-Jacobi method will be given. As a result compatible number will be obtained.},
 year = {2019}
}

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TY  - JOUR
T1  - Algebraic Modification of Trapezoidal Fuzzy Numbers to Complete Fully Fuzzy Linear Equations System Using Gauss-Jacobi Method
AU  - Ahmad Syaiful Abidin
AU  - Mashadi Mashadi
AU  - Sri Gemawati
Y1  - 2019/09/02
PY  - 2019
N1  - https://doi.org/10.11648/j.ijmfs.20190502.12
DO  - 10.11648/j.ijmfs.20190502.12
T2  - International Journal of Management and Fuzzy Systems
JF  - International Journal of Management and Fuzzy Systems
JO  - International Journal of Management and Fuzzy Systems
SP  - 40
EP  - 46
PB  - Science Publishing Group
SN  - 2575-4947
UR  - https://doi.org/10.11648/j.ijmfs.20190502.12
AB  - This paper will discuss algebraic modification of trapezoidal fuzzy numbers with a general form of fully fuzzy numbers is  with  is n × n fuzzy matrix,  fuzzy vector, and  unknown fuzzy vector. The concept used in this paper is define positive or negative fuzzy numbers determined by the area on the left side of the x-axis and the right side of the x-axis. Furthermore, the concept will be applied to the multiplication of two fully fuzzy trapezoidal numbers to produce a new algebra that can be applied to a system of linear equations. At the end, an example of multiplication two fully fuzzy trapezoidal numbers using the Gauss-Jacobi method will be given. As a result compatible number will be obtained.
VL  - 5
IS  - 2
ER  -

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Author Information

Ahmad Syaiful Abidin

Department of Mathematics, University of Riau, Pekanbaru, Indonesia
Mashadi Mashadi

Department of Mathematics, University of Riau, Pekanbaru, Indonesia
Sri Gemawati

Department of Mathematics, University of Riau, Pekanbaru, Indonesia

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Plain Text BibTeX RIS

APA Style

Ahmad Syaiful Abidin, Mashadi Mashadi, Sri Gemawati. (2019). Algebraic Modification of Trapezoidal Fuzzy Numbers to Complete Fully Fuzzy Linear Equations System Using Gauss-Jacobi Method. International Journal of Management and Fuzzy Systems, 5(2), 40-46. https://doi.org/10.11648/j.ijmfs.20190502.12

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ACS Style

Ahmad Syaiful Abidin; Mashadi Mashadi; Sri Gemawati. Algebraic Modification of Trapezoidal Fuzzy Numbers to Complete Fully Fuzzy Linear Equations System Using Gauss-Jacobi Method. Int. J. Manag. Fuzzy Syst. 2019, 5(2), 40-46. doi: 10.11648/j.ijmfs.20190502.12

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AMA Style

Ahmad Syaiful Abidin, Mashadi Mashadi, Sri Gemawati. Algebraic Modification of Trapezoidal Fuzzy Numbers to Complete Fully Fuzzy Linear Equations System Using Gauss-Jacobi Method. Int J Manag Fuzzy Syst. 2019;5(2):40-46. doi: 10.11648/j.ijmfs.20190502.12

Copy | Download

@article{10.11648/j.ijmfs.20190502.12,
  author = {Ahmad Syaiful Abidin and Mashadi Mashadi and Sri Gemawati},
  title = {Algebraic Modification of Trapezoidal Fuzzy Numbers to Complete Fully Fuzzy Linear Equations System Using Gauss-Jacobi Method},
  journal = {International Journal of Management and Fuzzy Systems},
  volume = {5},
  number = {2},
  pages = {40-46},
  doi = {10.11648/j.ijmfs.20190502.12},
  url = {https://doi.org/10.11648/j.ijmfs.20190502.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijmfs.20190502.12},
  abstract = {This paper will discuss algebraic modification of trapezoidal fuzzy numbers with a general form of fully fuzzy numbers is  with  is n × n fuzzy matrix,  fuzzy vector, and  unknown fuzzy vector. The concept used in this paper is define positive or negative fuzzy numbers determined by the area on the left side of the x-axis and the right side of the x-axis. Furthermore, the concept will be applied to the multiplication of two fully fuzzy trapezoidal numbers to produce a new algebra that can be applied to a system of linear equations. At the end, an example of multiplication two fully fuzzy trapezoidal numbers using the Gauss-Jacobi method will be given. As a result compatible number will be obtained.},
 year = {2019}
}

Copy | Download

TY  - JOUR
T1  - Algebraic Modification of Trapezoidal Fuzzy Numbers to Complete Fully Fuzzy Linear Equations System Using Gauss-Jacobi Method
AU  - Ahmad Syaiful Abidin
AU  - Mashadi Mashadi
AU  - Sri Gemawati
Y1  - 2019/09/02
PY  - 2019
N1  - https://doi.org/10.11648/j.ijmfs.20190502.12
DO  - 10.11648/j.ijmfs.20190502.12
T2  - International Journal of Management and Fuzzy Systems
JF  - International Journal of Management and Fuzzy Systems
JO  - International Journal of Management and Fuzzy Systems
SP  - 40
EP  - 46
PB  - Science Publishing Group
SN  - 2575-4947
UR  - https://doi.org/10.11648/j.ijmfs.20190502.12
AB  - This paper will discuss algebraic modification of trapezoidal fuzzy numbers with a general form of fully fuzzy numbers is  with  is n × n fuzzy matrix,  fuzzy vector, and  unknown fuzzy vector. The concept used in this paper is define positive or negative fuzzy numbers determined by the area on the left side of the x-axis and the right side of the x-axis. Furthermore, the concept will be applied to the multiplication of two fully fuzzy trapezoidal numbers to produce a new algebra that can be applied to a system of linear equations. At the end, an example of multiplication two fully fuzzy trapezoidal numbers using the Gauss-Jacobi method will be given. As a result compatible number will be obtained.
VL  - 5
IS  - 2
ER  -

Copy | Download