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Methods for solving LR-bipolar fuzzy linear systems

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Abstract

In this paper, we propose a technique to solve LR-bipolar fuzzy linear system(BFLS), LR-complex bipolar fuzzy linear (CBFL) system with real coefficients and LR-complex bipolar fuzzy linear (CBFL) system with complex coefficients of equations. Initially, we solve the LR-BFLS of equations using a pair of positive\((*)\) and negative\((\bullet )\) of two \(n \times n\) LR-real linear systems by using mean values and left-right spread systems. We also provide the necessary and sufficient conditions for the solution of LR-BFLS of equations. We illustrate the method by using some numerical examples of symmetric and asymmetric LR-BFLS equations and obtain the strong and weak solutions to the systems. Further, we solve the LR-CBFL system of equations with real coefficients and LR-CBFL system of equations with complex coefficients by pair of positive\((*)\) and negative\((\bullet )\) two \(n \times n\) real and complex LR-bipolar fuzzy linear systems by using mean values and left-right spread systems. Finally, we show the usage of technique to solve the current flow circuit which is represented by LR-CBFL system with complex coefficients and obtain the unknown current in term of LR-bipolar fuzzy complex number.

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Authors and Affiliations

  1. Department of Mathematics, University of the Punjab, New Campus, Lahore, Pakistan

    Muhammad Akram & Muhammad Ali

  2. Faculty of Engineering and Natural Sciences, Bahcesehir University, Istanbul, Turkey

    Tofigh Allahviranloo

  3. Department of Electrical and Computer Engineering, University of Alberta, Edmonton, Canada

    Witold Pedrycz

Authors
  1. Muhammad Akram
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  2. Tofigh Allahviranloo
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  3. Witold Pedrycz
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  4. Muhammad Ali
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Correspondence to Muhammad Akram.

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Communicated by A. Di Nola.

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Akram, M., Allahviranloo, T., Pedrycz, W. et al. Methods for solving LR-bipolar fuzzy linear systems. Soft Comput 25, 85–108 (2021). https://doi.org/10.1007/s00500-020-05460-z

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