Research Article
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Year 2023, Volume: 6 Issue: 1, 42 - 50, 29.03.2023
https://doi.org/10.33401/fujma.1195121

Abstract

Supporting Institution

Yok

Project Number

Yok

References

  • [1] S. Chanas, M. Nowakowski, Single value simulation of fuzzy variable, Fuzzy Sets Syst., 25(1) (1988), 43-57.
  • [2] J. Rohn, Inverse interval matrix, SIAM J. Numer. Anal., 30(3) (1993), 864-870.
  • [3] S. S. Rao, L. Chen, Numerical solution of fuzzy linear equations in engineering analysis, Int. J. Numer. Methods Eng., 42(5) (1998), 829-846.
  • [4] M. Dehghan, M. Ghatee, B. Hashemi, Inverse of a fuzzy matrix of fuzzy numbers, Int. J. Comput. Math., 86(8) (2009), 1433-1452.
  • [5] M. A. Basaran, Calculating fuzzy inverse matrix using fuzzy linear equation system, Appl. Soft Comput., 12(6) (2012), 1810-1813.
  • [6] M. Mosleh, Evaluation of fully fuzzy matrix equations by fuzzy neural network, Appl. Math. Modell., 37(9) (2013), 6364-6376.
  • [7] M. Mosleh, M. Otadi, A discussion on “Calculating fuzzy inverse matrix using fuzzy linear equation system”, Appl. Soft Comput., 28 (2015), 511-513.
  • [8] J. Kaur, A. Kumar, Commentary on “Calculating fuzzy inverse matrix using fuzzy linear equation system”, Appl. Soft Comput., 58 (2017), 324-327.
  • [9] X. Guo, Y. Wei, Z. Li, Further investigation to approximate fuzzy inverse, J. Intell. Fuzzy Syst., 35(1) (2018), 1161-1168.
  • [10] C. Y. Chen, J. J. Huang, Deriving fuzzy weights of the fuzzy analytic network process via fuzzy inverse matrix, Mathematics, 7(10) (2019), 914.
  • [11] F. Babakordi, N. A. Taghi-Nezhad, Calculating fuzzy inverse matrix using linear programming problem: An improved approach, Pak. J. Stat. Oper. Res. (2021), 983-996.
  • [12] H. Farahani, M. J. Ebadi, Finding fuzzy inverse matrix using Wu’s method, J. Mahani Math. Res. Cent., 10(1) (2021), 37-52.
  • [13] H. G. Akdemir, H. G. Kocken, A new fuzzy linear regression algorithm based on the simulation of fuzzy samples and an application on popularity prediction of Covid-19 related videos, J. Stat. Manage. Syst., 25(8) (2022), 2025-2041.
  • [14] P. V. Saraev, Interval pseudo-inverse matrices and interval Greville algorithm, Reliab. Comput., 18 (2013), 147-156.
  • [15] J. Lebedinska, On another view of an inverse of an interval matrix, Soft Comput., 14(10) (2010), 1043-1046.

Approximate Fuzzy Inverse Matrix Calculation Method using Scenario-based Inverses and Bisection

Year 2023, Volume: 6 Issue: 1, 42 - 50, 29.03.2023
https://doi.org/10.33401/fujma.1195121

Abstract

In this paper, we introduce a numerical method to construct the inverse of a square matrix whose elements are trapezoidal or triangular fuzzy numbers (FNs). A set of fuzzy linear equations is required to be solved in order to determine the fuzzy inverse matrix. The proposed technique first iteratively searches the possible solution intervals and then narrows those too-wide estimated intervals via bisection. Using interval arithmetic in left and right matrix multiplication, we aim to approximate the identity matrix as a result of product operations. The dissimilarity of the endpoints of intervals belonging to multiplication matrices with the identity matrix is considered to be an error function to be minimized. In this way, even if the entries of a matrix are uncertain, the fuzzy inverse matrix containing all inverse matrices can be found quickly with the use of computer technology. The method is explained, and comparisons are drawn with inverse stable examples from the literature.

Project Number

Yok

References

  • [1] S. Chanas, M. Nowakowski, Single value simulation of fuzzy variable, Fuzzy Sets Syst., 25(1) (1988), 43-57.
  • [2] J. Rohn, Inverse interval matrix, SIAM J. Numer. Anal., 30(3) (1993), 864-870.
  • [3] S. S. Rao, L. Chen, Numerical solution of fuzzy linear equations in engineering analysis, Int. J. Numer. Methods Eng., 42(5) (1998), 829-846.
  • [4] M. Dehghan, M. Ghatee, B. Hashemi, Inverse of a fuzzy matrix of fuzzy numbers, Int. J. Comput. Math., 86(8) (2009), 1433-1452.
  • [5] M. A. Basaran, Calculating fuzzy inverse matrix using fuzzy linear equation system, Appl. Soft Comput., 12(6) (2012), 1810-1813.
  • [6] M. Mosleh, Evaluation of fully fuzzy matrix equations by fuzzy neural network, Appl. Math. Modell., 37(9) (2013), 6364-6376.
  • [7] M. Mosleh, M. Otadi, A discussion on “Calculating fuzzy inverse matrix using fuzzy linear equation system”, Appl. Soft Comput., 28 (2015), 511-513.
  • [8] J. Kaur, A. Kumar, Commentary on “Calculating fuzzy inverse matrix using fuzzy linear equation system”, Appl. Soft Comput., 58 (2017), 324-327.
  • [9] X. Guo, Y. Wei, Z. Li, Further investigation to approximate fuzzy inverse, J. Intell. Fuzzy Syst., 35(1) (2018), 1161-1168.
  • [10] C. Y. Chen, J. J. Huang, Deriving fuzzy weights of the fuzzy analytic network process via fuzzy inverse matrix, Mathematics, 7(10) (2019), 914.
  • [11] F. Babakordi, N. A. Taghi-Nezhad, Calculating fuzzy inverse matrix using linear programming problem: An improved approach, Pak. J. Stat. Oper. Res. (2021), 983-996.
  • [12] H. Farahani, M. J. Ebadi, Finding fuzzy inverse matrix using Wu’s method, J. Mahani Math. Res. Cent., 10(1) (2021), 37-52.
  • [13] H. G. Akdemir, H. G. Kocken, A new fuzzy linear regression algorithm based on the simulation of fuzzy samples and an application on popularity prediction of Covid-19 related videos, J. Stat. Manage. Syst., 25(8) (2022), 2025-2041.
  • [14] P. V. Saraev, Interval pseudo-inverse matrices and interval Greville algorithm, Reliab. Comput., 18 (2013), 147-156.
  • [15] J. Lebedinska, On another view of an inverse of an interval matrix, Soft Comput., 14(10) (2010), 1043-1046.
There are 15 citations in total.

Details

Primary Language English
Subjects Computer Software, Mathematical Sciences
Journal Section Articles
Authors

Hande Günay Akdemir 0000-0003-3241-1560

Project Number Yok
Publication Date March 29, 2023
Submission Date October 26, 2022
Acceptance Date December 22, 2022
Published in Issue Year 2023 Volume: 6 Issue: 1

Cite

APA Günay Akdemir, H. (2023). Approximate Fuzzy Inverse Matrix Calculation Method using Scenario-based Inverses and Bisection. Fundamental Journal of Mathematics and Applications, 6(1), 42-50. https://doi.org/10.33401/fujma.1195121
AMA Günay Akdemir H. Approximate Fuzzy Inverse Matrix Calculation Method using Scenario-based Inverses and Bisection. Fundam. J. Math. Appl. March 2023;6(1):42-50. doi:10.33401/fujma.1195121
Chicago Günay Akdemir, Hande. “Approximate Fuzzy Inverse Matrix Calculation Method Using Scenario-Based Inverses and Bisection”. Fundamental Journal of Mathematics and Applications 6, no. 1 (March 2023): 42-50. https://doi.org/10.33401/fujma.1195121.
EndNote Günay Akdemir H (March 1, 2023) Approximate Fuzzy Inverse Matrix Calculation Method using Scenario-based Inverses and Bisection. Fundamental Journal of Mathematics and Applications 6 1 42–50.
IEEE H. Günay Akdemir, “Approximate Fuzzy Inverse Matrix Calculation Method using Scenario-based Inverses and Bisection”, Fundam. J. Math. Appl., vol. 6, no. 1, pp. 42–50, 2023, doi: 10.33401/fujma.1195121.
ISNAD Günay Akdemir, Hande. “Approximate Fuzzy Inverse Matrix Calculation Method Using Scenario-Based Inverses and Bisection”. Fundamental Journal of Mathematics and Applications 6/1 (March 2023), 42-50. https://doi.org/10.33401/fujma.1195121.
JAMA Günay Akdemir H. Approximate Fuzzy Inverse Matrix Calculation Method using Scenario-based Inverses and Bisection. Fundam. J. Math. Appl. 2023;6:42–50.
MLA Günay Akdemir, Hande. “Approximate Fuzzy Inverse Matrix Calculation Method Using Scenario-Based Inverses and Bisection”. Fundamental Journal of Mathematics and Applications, vol. 6, no. 1, 2023, pp. 42-50, doi:10.33401/fujma.1195121.
Vancouver Günay Akdemir H. Approximate Fuzzy Inverse Matrix Calculation Method using Scenario-based Inverses and Bisection. Fundam. J. Math. Appl. 2023;6(1):42-50.

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