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Fully fuzzy linear systems with trapezoidal and hexagonal fuzzy numbers

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Abstract

We study fully fuzzy linear systems with trapezoidal and hexagonal fuzzy numbers. The existence and uniqueness of the solution for such systems have been investigated in the literature under some restrictions on the coefficients matrix on one hand, and on the multiplication of fuzzy numbers on the other hand. Almost all researchers approximated the multiplication of two fuzzy numbers when they used the arithmetic \(\alpha -cut\). Using this approach, the multiplication of two positive fuzzy numbers need not be positive and in other times leads to a fuzzy number that is not of the same type. The aim of the current research is to solve trapezoidal and hexagonal fuzzy linear systems using the exact multiplication definition of \(\alpha -cut\) and under certain conditions on the coefficients matrices to insure that the solution is a set of positive fuzzy numbers that are trapezoidal and hexagonal, respectively. We illustrate the proposed method using a number of numerical examples. We compare the numerical results with a well-known method to show the advantages of the proposed method.

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Acknowledgements

We would like to thank the anonymous reviewers and our research group members for helpful discussions and comments. Moreover, we thank Arab American University-Palestine (AAUP) and Palestine Technical University-kadoorie (PTUK) for their continuous support.

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Authors and Affiliations

  1. Department of Mathematics and Statistics, Arab American University, 240 Jenin 13, Zababdeh, Palestine

    Abdelhalim Ziqan, Sabreen Ibrahim & Ammar Qarariyah

  2. Department of Applied Mathematics, Palestine Technical University-Kadoorie, Jaffa Street 7, Tulkarem, Palestine

    Mohammad Marabeh

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  1. Abdelhalim Ziqan
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  2. Sabreen Ibrahim
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  3. Mohammad Marabeh
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  4. Ammar Qarariyah
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Correspondence to Ammar Qarariyah.

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Ziqan, A., Ibrahim, S., Marabeh, M. et al. Fully fuzzy linear systems with trapezoidal and hexagonal fuzzy numbers. Granul. Comput. 7, 229–238 (2022). https://doi.org/10.1007/s41066-021-00262-6

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  • DOI: https://doi.org/10.1007/s41066-021-00262-6

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