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Bipolar fuzzy linear system of equations

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Abstract

A bipolar fuzzy set is a powerful tool for depicting fuzziness and uncertainty. This model is more flexible and practical as compared to the fuzzy model. In this paper, we define certain notions, including a bipolar fuzzy number in the parametric form, the distance between two bipolar fuzzy number and bipolar fuzzy arithmetic. We illustrate these concepts with examples. We discuss the system of linear equations and its solution process with the right-hand side as parametric bipolar fuzzy numbers, and obtain the strong solution of the system. Further, we analyze our new approach to find the solutions of a fully bipolar fuzzy linear system of equations (FBFLSE) which is based on \((-1,1)\)-cut expansion. Moreover, by utilizing the proposed method, we determine the maximal and minimal symmetric solutions of the FBFLSEs which are based on a tolerable solution set and a controllable solution set, respectively. We also present numerical examples of our proposed FBFLSE.

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Authors and Affiliations

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

    Muhammad Akram & Ghulam Muhammad

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

    Tofigh Allahviranloo

Authors
  1. Muhammad Akram
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  2. Ghulam Muhammad
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  3. Tofigh Allahviranloo
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Correspondence to Tofigh Allahviranloo.

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Communicated by Marcos Eduardo Valle.

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Akram, M., Muhammad, G. & Allahviranloo, T. Bipolar fuzzy linear system of equations. Comp. Appl. Math. 38, 69 (2019). https://doi.org/10.1007/s40314-019-0814-8

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  • DOI: https://doi.org/10.1007/s40314-019-0814-8

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