Skip to main content
SpringerLink
Log in

An improved solution for the neutrosophic linear programming problems based on Mellin’s transform

  • Fuzzy systems and their mathematics
  • Published:
Soft Computing Aims and scope Submit manuscript

Abstract

The aim of this paper is to develop a new de-neutrosophication technique for single-valued triangular neutrosophic (SVTrN) numbers using the method based on probability density function of the corresponding truth, an indeterminacy and falsity membership functions. Using the proposed ranking technique a methodology for solving neutrosophic linear programming problems involves SVTrN numbers. The method solution process for each objective is solved by independent to the set of individual value of the objectives decision maker’s. Then using the concept for comparison of SVTrN numbers, by the aid of the Mellin’s transform, we converted neutrosophic numbers into crisp numbers. Finally, the computational results and performance analysis of the proposed algorithm are presented.

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
Fig. 2

Similar content being viewed by others

Data availability

Enquiries about data availability should be directed to the authors.

References

  • Abdelfattah Walid (2020) A parametric approach to solve neutrosophic linear programming models. J Inf Optim Sci. https://doi.org/10.1080/02522667.2020.1764695

    Article  Google Scholar 

  • Abha Aggarwal, Aparna Mehra, Suresh Chandra, Imran Khan (2017) Solving I-fuzzy number linear programming problems via Tanaka and Asai approach. Notes Intuit Fuzzy Sets 23(5):85–101

    MATH  Google Scholar 

  • Alaulden NA, Sanar MY (2014) Solving fuzzy network problems by defuzzification techniques. Int J Innov Res Sci Eng Technol 3(11)

  • Amer AH (2019) Bi-level non-linear fractional programming problem with random fuzzy parameters, Int J Eng Sci Comput Vol. 9

  • Angelov PP (1997) Optimization in an intuitionistic fuzzy environment. Fuzzy Sets Syst 86:299–306. https://doi.org/10.1016/S0165-0114(96)00009-7

    Article  MathSciNet  MATH  Google Scholar 

  • Arpita Kabiraj, Kumar Nayak Prasun, Swapan Raha (2019) Solving intuitionistic fuzzy linear programming problem. Int J Intell Sci 9:44–58. https://doi.org/10.4236/ijis.2019.91003

    Article  Google Scholar 

  • Atanassov K (1999) Intuitionistic fuzzy sets: theory and applications. Physica-Verlag, Heidelberg, pp 1–137

    Book  Google Scholar 

  • Barik SK, Biswal MP (2012) Probabilistic quadratic programming problems with some fuzzy parameters. Adv Oper Res. https://doi.org/10.1155/2012/635282

    Article  MathSciNet  MATH  Google Scholar 

  • Basumatary B, Broumi S (2020) Interval- valued triangular neutrosophic linear programming problem. Int J Neutrosophic Sci 10(2):105–115

    Google Scholar 

  • Bera T, Mahapatra NK (2020) An approach to solve the linear programming problem using single valued trapezoidal neutrosophic number. Int J Neutrosophic Sci 3(2):54–66

    Article  Google Scholar 

  • Bera T, Mahapatra NK (2020b) Generalized single valued neutrosophic number and its application to neutrosophic linear programming, Neutrosophic Sets Syst, Vol. 25

  • Biswas A, De AK (2016) An efficient ranking technique for intuitionistic fuzzy numbers with its application in chance constrained bilevel programming. Adv Fuzzy Syst 10(1155/2016):6475403

    MathSciNet  MATH  Google Scholar 

  • Chakraborty Dipankar, Jana Dipak Kumar, Roy Tapan Kumar (2014) A new approach to solve intuitionistic fuzzy optimization problem using possibility, necessity, and credibility measures. Int J Eng Math. https://doi.org/10.1155/2014/593185

    Article  MATH  Google Scholar 

  • Darehmiraki Majid (2020) A solution for the neutrosophic linear programming problem with a new ranking function. Optim Theory Neutrosophic Plithogenic Sets. https://doi.org/10.1016/B978-0-12-819670-0.00011-1

    Article  Google Scholar 

  • Das SK, Dash JK (2020) Modified solution for neutrosophic linear programming problems with mixed constraints. Int J Res Ind Eng 9(1):13–24. https://doi.org/10.22105/riej.2020.224198.1127

    Article  Google Scholar 

  • Dubey D, Mehra A (2011) Linear programming with triangular intuitionistic fuzzy number. Proceedings of the 7th Conference of the European Society for Fuzzy Logic and Technology, pp. 563–569. Atlantis Press

  • Ebrahimnejad A, Nasseri SH, Lotfi FH, Soltanifar M (2010) A primal- dual method for linear programming problems with fuzzy variables. Eur J Ind Eng 4:189–209

    Article  Google Scholar 

  • Gong Yanbing, Xiang Lin, Yang Shuxin, Ma Hailiang (2019) A new method for ranking interval type-2 fuzzy numbers based on mellin transform. Int J Uncertain Fuzziness Knowl Syst. https://doi.org/10.1142/S0218488520500257

    Article  Google Scholar 

  • Hussian AN, Mohamed M, Abdel-Baset M, Smarandache F (2017) Neutrosophic linear programming problems, Neutrosophic Oper Res, Vol. 1

  • Jimenez M, Arenas M, Bilbao A, Rodrguez MV (2007) Linear programming with fuzzy parameters: an interactive method resolution. Eur J Ind Eng 177:1599–1606

    MathSciNet  MATH  Google Scholar 

  • Kabiraj A, Nayak PK, Raha S (2019) Solving intuitionistic fuzzy linear programming problem-II. Int J Intell Sci 9:93–110

    Article  Google Scholar 

  • Kiran Khatter (2020) Neutrosophic linear programming using possibilistic mean. Soft Comput. https://doi.org/10.1007/s00500-020-04980-y

    Article  Google Scholar 

  • Liu X (2001) Measuring the satisfication of constraints in fuzzy linear programming. Fuzzy Sets Syst 122:263–275

    Article  Google Scholar 

  • Maleki HR (2002) Ranking functions and their applications to FLP. Far East J Math Sci 4:283–301

    MATH  Google Scholar 

  • Maleki HR, Tata M, Mashinchi M (2000) Linear programming with fuzzy variables. Fuzzy Sets Syst 109:21-33

    Article  MathSciNet  Google Scholar 

  • Mohamed Abdel-Basset, Gunasekaran M, Mai Mohamed, Florentin Smarandache (2018) A novel method for solving the fully neutrosophic linear programming problems. Neural Comput Appl. https://doi.org/10.1007/s00521-018-3404-6

    Article  Google Scholar 

  • Nafei Amirhossein, Yuan Wnjun, Nasseri Hadi (2020) A new method for solving interval neutrosophic linear programming problems. J Sci. https://doi.org/10.35378/gujs.689125

    Article  Google Scholar 

  • Nasseri SH (2008) A new method for solving fuzzy linear programming by solving linear programming. Appl Math Sci 2:2473–2480

    MathSciNet  MATH  Google Scholar 

  • Nishad AK, Singh SR (2014) Linear programming problem with intuitionistic fuzzy numbers. Int J Comput Appl 106:22–28

    Google Scholar 

  • Paravathi R, Malathi C (2012) Intuitionistic fuzzy linear programming problem. World Appl Sci J 17:1802–1807

    Google Scholar 

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

    MATH  Google Scholar 

  • Peraei EY, Maleki HR, Mashinchi M (2001) A method for solving a fuzzy linear programming. Korean J Comput Appl Math 8(2):347–356

    Article  MathSciNet  Google Scholar 

  • Rahim Saneifard, Rasoul Saneifard (2011) A modified method for defuzzification by probability density function. J Appl Sci Res 7(2):102–110

    Google Scholar 

  • Robinson MJ, Veeramani C, Vasanthi S (2019) A new approach for solving intuitionistic fuzzy optimization problems. Tierarztliche Praxis 39(11):135–159

  • Sagayakavitha D, Sudha S (2020), New approach to solve symmetric triangular neutrosophic linear programming problem by score function, J Inf Comput Sci, Vol. 10

  • Saneifard R, Asghary A (2011) A method for defuzzification based on probability density function (II). Appl Math Sci 5(28):1357–1365

    MathSciNet  MATH  Google Scholar 

  • Singh A, Kumar A, Appadoo SS (2019) A novel method for solving the fully neutrosophic linear programming problems: suggested modifications. J Intell Fuzzy Syst 37:885–895. https://doi.org/10.3233/JIFS-181541

    Article  Google Scholar 

  • Tanaka H, Okuda T, Asai K (1974) On fuzzy mathematical programming. Cybern J 3(4):37–46

    Article  MathSciNet  Google Scholar 

  • Tuhin Bera, Kumar Mahapatra Nirmal (2019) Neutrosophic linear programming problem and its application to real life. Afrika Matematika. https://doi.org/10.1007/s13370-019-00754-4

    Article  Google Scholar 

  • Wang H, Smarandache F, Zhang YQ, Sunderraman R (2005) Interval neutrosophic sets and logic. Theory and applications in computing. Hexis, France

    MATH  Google Scholar 

  • Wang H, Smarandache F, Zhang Y, Sunderraman R (2010) Single valued neutrosophic sets. Multi space and Multi structure

  • Yoon KP (1996) A probabilistic approach to rank complex fuzzy numbers. Fuzzy Sets Syst 80:167–176

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

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

    Article  MathSciNet  Google Scholar 

Download references

Funding

The authors have not disclosed any funding.

Author information

Author notes

  1. S. Paulraj has contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics, College of Engineering Guindy, Anna University, Chennai, Tamil Nadu, 600025, India

    G. Tamilarasi & S. Paulraj

Authors
  1. G. Tamilarasi
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. S. Paulraj
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to G. Tamilarasi.

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

Publisher's Note

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

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Tamilarasi, G., Paulraj, S. An improved solution for the neutrosophic linear programming problems based on Mellin’s transform. Soft Comput 26, 8497–8507 (2022). https://doi.org/10.1007/s00500-022-07252-z

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00500-022-07252-z

Keywords

Search

Navigation