Modified Cramer's rule for solving a fully fuzzy system of linear equations with a nonsquare coefficient matrix

Fatema Khatun; Md Sahadat Hossain; Mst Monjuara Akter

doi:10.3329/jbas.v48i2.69400

Modified Cramer's rule for solving a fully fuzzy system of linear equations with a nonsquare coefficient matrix

Authors

Fatema Khatun Department of Computer Science and Engineering, Northern University Bangladesh, Dhaka, Bangladesh.
Md Sahadat Hossain Department of Mathematics, University of Rajshahi, Rajshahi, Bangladesh.
Mst Monjuara Akter Department of Mathematics, University of Rajshahi, Rajshahi, Bangladesh.

DOI:

https://doi.org/10.3329/jbas.v48i2.69400

Keywords:

Fully fuzzy system of Linear equations, triangular LR fuzzy Number, trapezoidal LR fuzzy number, Determinant of square and non-square matrix

Abstract

In this modern technological world, several problems arise daily, whose maximum problems have been unsolved in a classical way because of their ambiguity. To solve those problems, the applications of fuzzy mathematics are increasing rapidly, whereas traditional classical methods have failed. Here, we have modified Cramer's rules method for solving the non-square coefficient matrix of the fully fuzzy system of linear equations (FFSLE) using triangular and trapezoidal LR fuzzy numbers. This modified method is compared with another method that can only solve the square coefficient matrix using fuzzy triangular and trapezoidal numbers. At last, we observe that our modified method is more general than others. This process is illustrated with numerical examples.

J. Bangladesh Acad. Sci. 48(2); 147-160: December 2024

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Published

2024-12-31

How to Cite

Khatun, F., Hossain, M. S., & Akter, M. M. (2024). Modified Cramer’s rule for solving a fully fuzzy system of linear equations with a nonsquare coefficient matrix. Journal of Bangladesh Academy of Sciences, 48(2), 147–160. https://doi.org/10.3329/jbas.v48i2.69400