International Journal of Management and Fuzzy Systems

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

Received: Jul. 20, 2019    Accepted: Aug. 19, 2019    Published: Sep. 02, 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.

DOI 10.11648/j.ijmfs.20190502.12
Published in International Journal of Management and Fuzzy Systems ( Volume 5, Issue 2, June 2019 )
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), 2024. Published by Science Publishing Group

Keywords

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

References
[1] T. Allahviranloo, S. Salahshour, M. Homayoun-Nejad dan D. Beleanu, General solution of fully fuzzy systems, Abstract and Applied Analysis, 2013, 2013, 1-9.
[2] A. jafarian, New decomposition method for solving dual fully fuzzy linear system, Imt. Journal Fuzzy Computation and Modelling, 2, 2016, 76-85.
[3] M. Deghan dan B. Hashemi, Iterative solution of fuzzy linear system, Applied Mathematics and Computation, 175, 2006, 645-674.
[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.
[5] G. Malkawi, N. Ahmad dan H. Ibrahim, Solving fully fuzzy linear sys tem with the necessary an suficient to have a positive solution, Applied Mathematics and Information Sciences, 8, 2014, 1003-1019.
[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.
[8] N. J. Karthik dan E. Chandrasekaran, Solving fully fuzzy linear system with trapezoidal fuzzy number matrices by partitioning, International Jo- urnal of Computer Applications, 64, 2013, 35-38.
[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.
[11] A. Kumar and J. Kaur, Comentary on “Calculating fuzzy inverse matrix using fuzzy linear equation system”, Applied Soft Computing, 58, 2017, 324-327.
[12] L. A. Zadeh, Fuzzy Sets, Information and Control, 8, 1965, 338-353.
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[14] Mashadi, A new method for dual fully fuzzy linier system by use LU factorizations of the coeficient matrix, Jurnal Matematika dan Sains, 15, 2010, 101-106.
[15] S. Moloudzadeh, P. Darabi dan H. Khandani, The pseudo invers matrices to solve general fully fuzzy linear system, Journal of Soft Computing and Applications, 2013, 2013, 1-11.
[16] S. H. Nasheri dan M. Gholami, Linear system of equation with trapezoidal fuzzy numbers, The Journal of Mathematics and Computer Science, 3, 2011, 71-79.
[17] S. Das dan S. Chakraverty, Numerical solution of fuzzy system of linear equation, Applications and Applied Mathematics, 7, 2012, 334-356.
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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://download.sciencepg.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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    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
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    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
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    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
  • Department of Mathematics, University of Riau, Pekanbaru, Indonesia

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

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

  • Section