Skip to main content
SpringerLink
Log in

Methods for solving LR-bipolar fuzzy linear systems

  • Foundations
  • Published:
Soft Computing Aims and scope Submit manuscript

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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1

Similar content being viewed by others

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 (2011) Bipolar fuzzy graphs. Inf Sci 24(181):5548–5564

    Article  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

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  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

    Article  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

    Article  Google Scholar 

  • Akram M, Sarwar M, Dudek WA (2021) Graphs for the analysis of bipolar fuzzy information. Stud Fuzz Soft Comput 401:1–452

    Article  Google Scholar 

  • Akram M, Ali M, Allahviranloo T (2020a) Certain methods to solve bipolar fuzzy linear system of equations. Comput Appl Math 39:213

    Article  MathSciNet  MATH  Google Scholar 

  • Akram M, Muhammad G, Allahviranloo T, Hussain N (2020b) LU decomposition method to solve bipolar fuzzy linear systems. J Intell Fuzzy Syst 39(3):3329–3349

    Article  Google Scholar 

  • Allahviranloo T, Otadi M, Mosleh M (2008) Iterative method for fuzzy equations. Soft Comput 12(10):935–939

    Article  MATH  Google Scholar 

  • Allahviranloo T, Hosseinzadeh AA, Ghanbari M, Haghi E, Nuraei R (2014) On the new solutions for a fully fuzzy linear system. Soft Comput 18(1):95–107

    Article  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. Studies in systems, decision and control, vol 254. Springer, Berlin

  • Allahviranloo T, Hosseinzadeh F, Khorasani M, Khezerloo M (2013) On the fuzzy solution of LR fuzzy linear systems. Appl Math Model 37(3):1170–1176

    Article  MathSciNet  MATH  Google Scholar 

  • Alghamdi MA, Alshehri NO, Akram M (2018) Multi-criteria decision-making methods in bipolar fuzzy environment. Int J Fuzzy System 20(6):2057–2064

    Article  Google Scholar 

  • Amirfakhrian M (2012) Analyzing the solution of a system of fuzzy linear equations by a fuzzy distance. Soft Comput 16(6):1035–1041

    Article  MATH  Google Scholar 

  • Amirfakhrian M, Fallah M, Rodriguez-Lopez R (2018) A method for solving fuzzy matrix equations. Soft Comput 22:2095–2103

    Article  MATH  Google Scholar 

  • Behera D, Chakraverty S (2012) A new method for solving real and complex fuzzy systems of linear equations. Comput Math Model 23(4):507–518

    Article  MathSciNet  MATH  Google Scholar 

  • Buckley JJ (1989) Fuzzy complex number. Fuzzy Sets Syst 33:333–345

    Article  MathSciNet  MATH  Google Scholar 

  • Dehghan M, Hashemi B, Ghatee M (2007) Solution of fully fuzzy linear systems using iterative techniques. Chaos Solitons Fractals 34(2):316–336

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Ezzati R (2011) Solving fuzzy linear systems. Soft Comput 15(1):193–197

    Article  MathSciNet  MATH  Google Scholar 

  • Fariborzi Araghi MA, Fallahzadeh A (2013) Inherited LU factorization for solving fuzzy system of linear equations. Soft Comput 17(1):159–163

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  • Ghanbari M, Allahviranloo T, Pedrycz W (2020) On the rectangular fuzzy complex linear systems. Appl Soft Comput 91:106196

    Article  Google Scholar 

  • Guo X, Zhang K (2016) Minimal solution of complex fuzzy linear systems. Adv Fuzzy Syst 2016:9. https://doi.org/10.1155/2016/5293917

    Article  MathSciNet  MATH  Google Scholar 

  • Jahantigh MA, Khezerloo S, Khezerloo M (2010) Complex fuzzy linear systems. Int J Ind Math 2(1):21–28

    Google Scholar 

  • Koam NA, Akram M, Muhammad G, Hussain N (2020) LU decomposition scheme for solving m-polar fuzzy system of linear equations. Math Problems Eng Article ID 8384593

  • Jha A (2018) Meromorphic function of fuzzy complex variables. J New Theory 20:1–12

    Google Scholar 

  • Moloudzadeh S, Allahviranloo T, Darabi P (2013) A new method for solving an arbitrary fully fuzzy linear system. Soft Comput 17(9):1725–1731

    Article  MATH  Google Scholar 

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

    MATH  Google Scholar 

  • Rahgooy T, Yazdi HS, Monsefi R (2009) Fuzzy complex system of linear equations applied to circuit analysis. Int J Comput Electr Eng 1(5):535

    Article  Google Scholar 

  • Rao C, Lin H, Liu M (2020a) Design of comprehensive evaluation index system for P2P credit risk of three rural borrowers. Soft Comput 24:11493–11509

    Article  Google Scholar 

  • Rao C, Liu M, Goh M, Wen J (2020b) 2-stage modified random forest model for credit risk assessment of P2P network lending to Three Rurals borrowers. Appl Soft Comput 95:106570

    Article  Google Scholar 

  • Saqib M, Akram M, Shahida B, Allahviranloo T (2020a) Numerical solution of bipolar fuzzy initial value problem. J Intell Fuzzy Syst. https://doi.org/10.3233/JIFS201619

    Article  Google Scholar 

  • Saqib M, Akram M, Shahida B (2020b) Certain efficient iterative methods for bipolar fuzzy system of linear equations. J Intell Fuzzy Syst 39(3):3971–3985

    Article  Google Scholar 

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

    Article  MATH  Google Scholar 

  • Zadeh LA (1971) Similarity relations and fuzzy orderings. Inf Sci 3(2):177–200

    Article  MathSciNet  MATH  Google Scholar 

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

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

  • Zhang, W. R.: YinYang Bipolar fuzzy sets, Fuzzy Systems Proceedings, IEEE World Congress on Computational Intelligence, (1998), 835-840

  • Zheng B, Wang K (2006) Inconsistent fuzzy linear systems. Appl Math Comput 181:973–981

    MathSciNet  MATH  Google Scholar 

Download references

Author information

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
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Tofigh Allahviranloo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Witold Pedrycz
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Muhammad Ali
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Muhammad Akram.

Ethics declarations

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals performed by any of the authors.

Additional information

Communicated by A. Di Nola.

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

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

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-020-05460-z

Keywords

Search

Navigation