iBet uBet web content aggregator. Adding the entire web to your favor.
iBet uBet web content aggregator. Adding the entire web to your favor.



Link to original content: https://unpaywall.org/10.1007/S40314-021-01503-9
Fully Pythagorean fuzzy linear programming problems with equality constraints | Computational and Applied Mathematics Skip to main content
Springer Nature Link
Log in

Fully Pythagorean fuzzy linear programming problems with equality constraints

  • Published:
Computational and Applied Mathematics Aims and scope Submit manuscript

Abstract

There are several daily life problems where we have to deal with the uncertainties and we are forced to solve the uncertain linear programming models. Certain methods have been presented for dealing with linear programming problems based on fuzzy sets and intuitionistic fuzzy sets which are characterized by membership degree, membership and non-membership degrees, respectively. In this study, we first extend the concept of crisp linear programming problem in Pythagorean fuzzy environment based on triangular Pythagorean fuzzy numbers. The profit/cost coefficients in objective function, input/output coefficients and right-hand side coefficients and decision variables of a linear programming problem are considered as triangular Pythagorean fuzzy numbers. Further, we present methods for solving fully Pythagorean fuzzy linear programming problems for non-negative and unrestricted triangular Pythagorean fuzzy numbers with equality constraints. We also apply the proposed technique to solve practical models.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

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

    Article  Google Scholar 

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

    MathSciNet  MATH  Google Scholar 

  • Allahviranloo T, Lotfi FH, Kiasary MK, Kiani NA, Zadeh LA (2008) Solving fully fuzzy linear programming problem by the ranking function. Appl Math Sci 2(1):19–32

    MathSciNet  MATH  Google Scholar 

  • An JJ, Li DF (2019) A linear programming approach to solve constrained bi-matrix games with intuitionistic fuzzy payoffs. Int J Fuzzy Syst 21(3):908–915

    MathSciNet  Google Scholar 

  • Angelov PP (1997) Optimization in an intuitionistic fuzzy environment. Fuzzy Sets Syst 86(3):299–306

    MathSciNet  MATH  Google Scholar 

  • Atanassov KT (1986) Intuitionistic fuzzy sets. Fuzzy Sets Syst 20:87–96

    MATH  Google Scholar 

  • Bellman RE, Zadeh LA (1970) Decision making in a fuzzy environment. Manage Sci 17:141–164

  • Behera D, Peters K, Edalatpanah SA, Qiu D (2020) New methods for solving imprecisely defined linear programming problem under trapezoidal fuzzy uncertainty. J Inf Optim Sci. https://doi.org/10.1080/02522667.2020.1758369

    Article  Google Scholar 

  • Bharati SK, Singh SR (2019) Solution of multiobjective linear programming problems in interval-valued intuitionistic fuzzy environment. Soft Comput 23(1):77–84

    MATH  Google Scholar 

  • Chen TY (2021) Pythagorean fuzzy linear programming technique for multidimensional analysis of preference using a squared-distance-based approach for multiple criteria decision analysis. Expert Syst Appl 164:113908

    Google Scholar 

  • Dubey D, Mehra A (2011) Linear programming with triangular intuitionistic fuzzy number. Adv Intell Syst Res 1(1):563–569

    MATH  Google Scholar 

  • Edalatpanah SA (2019) A data envelopment analysis model with triangular intuitionistic fuzzy numbers. Int J Data Envel Anal 7(4):47–58

    MathSciNet  Google Scholar 

  • Garg H, Rani M, Sharma SP, Vishwakarma Y (2014) Intuitionistic fuzzy optimization technique for solving multi-objective reliability optimization problems in interval environment. Expert Syst Appl 41(7):3157–3167

    Google Scholar 

  • Garg H (2020) Linguistic interval-valued Pythagorean fuzzy sets and their application to multiple attribute group decision-making process. Cogn Comput 12:1313–1337

    Google Scholar 

  • Garg H (2020) A new possibility degree measure for interval-valued q-rung orthopair fuzzy sets in decision-making. Int J Intell Syst 36(1):526–557

    Google Scholar 

  • Kabiraj A, Nayak PK, Raha S (2019) Solving intuitionistic fuzzy linear programming problem. Int J Intell Sci 9:44–58

    Google Scholar 

  • Kaur J, Kumar A (2016) An introduction to fuzzy linear programming problems. Springer Science and Business Media LLC, New York

    Google Scholar 

  • Kaur J, Kumar A (2012) Exact fuzzy optimal solution of fully fuzzy linear programming problems with unrestricted fuzzy variables. Appl Intell 37:145–154

    Google Scholar 

  • Kumar A, Kaur J, Singh P (2011) A new method for solving fully fuzzy linear programming problems. Appl Math Model 35:817–823

    MathSciNet  MATH  Google Scholar 

  • Kumar R, Edalatpanah SA, Jha S, Singh R (2019) A Pythagorean fuzzy approach to the transportation problem. Complex Intell Syst 5:255–263

    Google Scholar 

  • Lotfi FH, Allahviranloo T, Jondabeh MA, Zadeh LA (2009) Solving a full fuzzy linear programming using lexicography method and fuzzy approximate solution. Appl Math Model 33(7):3151–3156

    MathSciNet  MATH  Google Scholar 

  • Luqman A, Akram M, Alcantud JCR (2020) Digraph and matrix approach for risk evaluations under Pythagorean fuzzy information. Expert Syst Appl 170:114518

    Google Scholar 

  • Mahapatra GS, Roy TK (2009) Reliability evaluation using triangular intuitionistic fuzzy numbers arithmetic operations. World Acad Sci Eng Technol 50:574–581

    Google Scholar 

  • Mahapatra GS, Roy TK (2013) Intuitionistic fuzzy number and its arithmetic operation with application on system failure. J Uncertain Syst 7(2):92–107

    Google Scholar 

  • Malathi C, Umadevi P (2018) A new procedure for solving linear programming problems in an intuitionistic fuzzy environment. IOP Conf Ser J Phys Conf Ser 1139:012079

    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

    MATH  Google Scholar 

  • Nagoorgani A, Ponnalagu K (2012) A new approach on solving intuitionistic fuzzy linear programming problem. Appl Math Sci 6(70):3467–3474

    MathSciNet  MATH  Google Scholar 

  • Nagoorgani A, Kavikumar J, Ponnalagu K (2015) The knowledge of expert opinion in intuitionistic fuzzy linear programming problem. Math Probl Eng 201:8. https://doi.org/10.1155/2015/875460 (article ID 875460)

  • Najafi HS, Edalatpanah SA (2013) A note on “A new method for solving fully fuzzy linear programming problems”. Appl Math Model 37(14–15):7865–7867

    MathSciNet  MATH  Google Scholar 

  • Najafi HS, Edalatpanah SA, Dutta H (2016) A nonlinear model for fully fuzzy linear programming with fully unrestricted variables and parameters. Alex Eng J 55(3):2589–2595

    Google Scholar 

  • Parvathi R, Malathi C (2012) Intuitionistic fuzzy linear optimization. Notes Intuit Fuzzy Sets 18(1):48–56

    MATH  Google Scholar 

  • Parvathi R, Malathi C, Akram M, Atanassov KT (2013) Intuitionistic fuzzy linear regression analysis. Fuzzy Optim Decis Mak 12(2):215–229

    MathSciNet  MATH  Google Scholar 

  • Parvathi R, Malathi C (2012) Intuitionistic fuzzy linear programming problems. World Appl Sci J 17(12):1787–1791

    MATH  Google Scholar 

  • Peng X, Yang Y (2015) Some results for Pythagorean fuzzy sets. Int J Intell Syst 30(11):1133–1160

    MathSciNet  Google Scholar 

  • Peng X, Yuan H, Yang Y (2017) Pythagorean fuzzy information measures and their applications. Int J Intell Syst 32(10):991–1029

    Google Scholar 

  • Pérez-Cañedo B, Concepción-Morales ER (2019) On \(LR\)-type fully intuitionistic fuzzy linear programming with inequality constraints: solutions with unique optimal values. Expert Syst Appl 128:246–255

    Google Scholar 

  • Pérez-Cañedo B, Concepción-Morales ER, Edalatpanah SA (2020) A revised version of a lexicographical-based method for solving fully fuzzy linear programming problems with inequality constraints. Fuzzy Inf Eng. https://doi.org/10.1080/16168658.2020.1761511

    Article  Google Scholar 

  • Rani D, Garg H (2021) Complex intuitionistic fuzzy preference relations and their applications in individual and group decision-making problems. Int J Intell Syst 36(4):1800–1830

    Google Scholar 

  • Saqib M, Akram M, Shahida B, Allahviranloo T (2021) Numerical solution of bipolar fuzzy initial value problem. Int J Artif Intell Expert Syst 40(1):1309–1341

    Google Scholar 

  • Singh SK, Yadav SP (2018) Intuitionistic fuzzy multi-objective linear programming problem with various membership functions. Ann Oper Res 269(1–2):693–707

    MathSciNet  MATH  Google Scholar 

  • Suresh M, Vengataasalam S, Arun PK (2014) Solving intuitionistic fuzzy linear programming problems by ranking function. J Intell Fuzzy Syst 27(6):3081–3087

    MathSciNet  MATH  Google Scholar 

  • Wan SP, Jin Z, Dong JY (2020) A new order relation for Pythagorean fuzzy numbers and application to multi-attribute group decision making. Knowl Inf Syst 62:751–785

    Google Scholar 

  • Wan SP, Jin Z, Dong JY (2018) Pythagorean fuzzy mathematical programming method for multi-attribute group decision making with Pythagorean fuzzy truth degrees. Knowl Inf Syst 55:437–466

    Google Scholar 

  • Xue W, Xu Z, Zhang X, Tian X (2018) Pythagorean fuzzy LINMAP method based on the entropy theory for railway project investment decision making. Int J Intell Syst 33(1):93–125

    Google Scholar 

  • Yager RR (2013) Pythagorean fuzzy subsets. In: Proceedings of the Joint IFSA World Congress and NAFIPS Annual Meeting, Edmonton, Canada, pp 57–61

  • Yager RR, Abbasov AM (2013) Pythagorean membership grades, complex numbers and decision making. Int J Intell Syst 28(5):436–452

    Google Scholar 

  • Yager RR (2014) Pythagorean membership grades in multi-criteria decision making. IEEE Trans Fuzzy Syst 22(4):958–965

    Google Scholar 

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

    MATH  Google Scholar 

  • Zhang X, Xu Z (2014) Extension of TOPSIS to multiple-criteria decision making with Pythagorean fuzzy sets. Int J Intell Syst 29(12):1061–1078

    Google Scholar 

  • Zimmerman HJ (1978) Fuzzy programming and linear programming with several objective functions. Fuzzy Set Syst 1:45–55

Download references

Author information

Authors and Affiliations

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

    Muhammad Akram & Inayat Ullah

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

    Tofigh Allahviranloo

  3. Department of Applied Mathematics, Ayandegan Institute of Higher Education, Tonekabon, Iran

    S. A. Edalatpanah

Authors
  1. Muhammad Akram
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Inayat Ullah
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Tofigh Allahviranloo
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. S. A. Edalatpanah
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to S. A. Edalatpanah.

Ethics declarations

Conflict of interest

The authors declare no conflict of interest.

Additional information

Communicated by Marcos Eduardo Valle.

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., Ullah, I., Allahviranloo, T. et al. Fully Pythagorean fuzzy linear programming problems with equality constraints. Comp. Appl. Math. 40, 120 (2021). https://doi.org/10.1007/s40314-021-01503-9

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1007/s40314-021-01503-9

Keywords

Mathematics Subject Classification

Search

Navigation