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The Fuzzy Complex Linear Systems Based on a New Representation of Fuzzy Complex Numbers

Author

Listed:
  • Zhiyong Xiao

    (School of Mathematics and Statistics, Longdong University, Qingyang 745000, China)

  • Zengtai Gong

    (College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730000, China)

Abstract

Since the product of complex numbers and rectangular fuzzy complex numbers (RFCN) is not necessarily a RFCN in the former fuzzy complex linear system (FCLS), the scalar multiplication and addition operations of complex numbers and fuzzy complex numbers (FCN) based on a new representation of FCN are proposed. We also introduce a new method for solving FCLS, which can convert FCLS into two distinct linear systems. One is an n × n complex linear system, and the other is an ( m n ) × ( m n ) real linear system, where n is the number of unknown variables, and m is the number of substitutional cyclic sets composed of coefficients of FCLS. In particular, using this method to solve one-dimensional fuzzy linear systems, a ( 2 n ) × ( 2 n ) RLS is obtained, which is consistent with Friedman’s method. Finally, FCLS based on the RFCN as a special case are also investigated.

Suggested Citation

  • Zhiyong Xiao & Zengtai Gong, 2022. "The Fuzzy Complex Linear Systems Based on a New Representation of Fuzzy Complex Numbers," Mathematics, MDPI, vol. 10(15), pages 1-14, August.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:15:p:2822-:d:883349
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    References listed on IDEAS

    as
    1. Dehghan, Mehdi & Hashemi, Behnam & Ghatee, Mehdi, 2007. "Solution of the fully fuzzy linear systems using iterative techniques," Chaos, Solitons & Fractals, Elsevier, vol. 34(2), pages 316-336.
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