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Certain methods to solve bipolar fuzzy linear system of equations

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Abstract

In this article, we present two different analytical methods based on embedding technique and bipolar fuzzy center to solve bipolar fuzzy linear system (BFLS) of equations. In the first method, to solve BFLS of equations, we replace BFLS of equations by a pair of positive\((*)\) and negative\((\bullet )\) two \(n \times n\) crisp linear systems. We provide the necessary and sufficient conditions for the solution of BFLS of equations. In the second method, we use the graphical technique and apply bipolar fuzzy center to draw a graph at some specific end points to solve the BFLS of equations. Further, we develop a technique to solve the fully bipolar fuzzy linear system of equations. We present solutions of some numerical examples to show the effectiveness of the proposed techniques.

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References

  • Abbasbandy S, Alavi M (2005) A method for solving fuzzy linear systems. Fuzzy Sets Syst 2(2):37–43

    MathSciNet  MATH  Google Scholar 

  • Abbasbandy S, Jafarian A (2006) Steepest descent method for system of fuzzy linear equations. Appl Math Comput 175(1):823–833

    MathSciNet  MATH  Google Scholar 

  • Akram M, Arshad M (2019) A novel trapezoidal bipolar fuzzy TOPSIS method for group decision-making. Group Decis Negot 28(3):565–584

    Google Scholar 

  • Akram M, Muhammad G, Koam AN, Hussain N (2019a) Iterative methods for solving a system of linear equations in a bipolar fuzzy environment. Mathematics 7(8):728

    Google Scholar 

  • Akram M, Muhammad G, Allahviranloo T (2019b) Iterative methods for solving a system of linear equations in a bipolar fuzzy environment. Mathematics 7(8):728

    Google Scholar 

  • Akram M, Muhammad G, Hussian N (2019c) Bipolar fuzzy system of linear equations with polynomial parametric form. J Intell Fuzzy Syst 37(6):8275–8287

    Google Scholar 

  • Akram M, Saleem D, Allahviranloo T (2019d) Linear system of equations in m-polar fuzzy environment. J Intell Fuzzy Syst 37(6):8251–8266

    Google Scholar 

  • Akram M, Muhammad G, Allahviranloo T (2019e) Bipolar fuzzy linear system of equations. Comput Appl Math 38(2):69

    MathSciNet  MATH  Google Scholar 

  • Allahviranloo T (2004) Numerical methods for fuzzy system of linear equations. Appl Math Comput 155(2):493–502

    MathSciNet  MATH  Google Scholar 

  • Allahviranloo T (2005a) Successive over relaxation iterative method for fuzzy system of linear equations. Appl Math Comput 162(1):189–196

    MathSciNet  MATH  Google Scholar 

  • Allahviranloo T (2005b) The Adomian decomposition method for fuzzy system of linear equations. Appl Math Comput 163(2):553–563

    MathSciNet  MATH  Google Scholar 

  • Allahviranloo T (2019) Uncertain information and linear systems, studies in systems, decision and control. Springer, Berlin, p 254

    Google Scholar 

  • Dubois D, Prade H (1978) Operations on fuzzy numbers. Int J Syst Sci 9:613–626

    MathSciNet  MATH  Google Scholar 

  • Friedman M, Ming MMa, Kandel A (1998) Fuzzy linear systems. Fuzzy Sets Syst 96:201–209

    MathSciNet  MATH  Google Scholar 

  • Minc H (1988) Nonnegative matrices. Wiley, New York

    MATH  Google Scholar 

  • Ming M, Friedman M, Kandel A (1999) A new fuzzy arithmetic. Fuzzy Sets Syst 108(1):83–90

    MathSciNet  MATH  Google Scholar 

  • Senthilkumar P, Rajendran G (2009) Solution of fuzzy linear systems by using fuzzy centre. Appl Math Sci 3(49):2411–2419

    MathSciNet  MATH  Google Scholar 

  • Suparna D, Chakraverty S (2011) Numerical solution of interval and fuzzy system of linear equations. Doctoral dissertation

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353

    MATH  Google Scholar 

  • Zadeh LA (1975) The concept of a linguistic and application to approximate reasoning-I. Inf Sci 8:199–249

    MathSciNet  MATH  Google Scholar 

  • Zhang WR (1994) Bipolar fuzzy sets and relations: a computational framework forcognitive modeling and multiagent decision analysis. In: Proceedings of IEEE conference, pp 305–309

  • Zhang WR (1998) YinYang Bipolar fuzzy sets. In: IEEE world congress on fuzzy systems proceedings. Computational Intelligence, pp 835–840

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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

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

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Communicated by Leonardo Tomazeli Duarte.

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Akram, M., Ali, M. & Allahviranloo, T. Certain methods to solve bipolar fuzzy linear system of equations. Comp. Appl. Math. 39, 213 (2020). https://doi.org/10.1007/s40314-020-01256-x

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  • DOI: https://doi.org/10.1007/s40314-020-01256-x

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