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Mehar approach to solve fuzzy linear fractional transportation problems

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Abstract

To the best of author’s knowledge, only three approaches are proposed in the literature to solve fully fuzzy linear fractional transportation problems. (Linear fractional transportation problems in which each known parameter is represented by a fuzzy number.) In this paper, it is pointed out that it is inappropriate to use any of these existing approaches as some mathematical incorrect assumptions are considered in these existing approaches. Also, a new approach (named as Mehar approach) is proposed to solve fully fuzzy linear fractional transportation problems. Furthermore, an exact fuzzy optimal solution of an existing fully fuzzy linear fractional transportation problem is obtained by the proposed Mehar approach.

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References

  • Abualigah L, Yousri D, Abd Elaziz M, Ewees AA, Al-qaness MA, Gandomi AH (2021a) Aquila optimizer: a novel meta-heuristic optimization algorithm. Comput Ind Eng 157:107250

    Article  Google Scholar 

  • Abualigah L, Diabat A, Mirjalili S, Abd Elaziz M, Gandomi AH (2021b) The arithmetic optimization algorithm. Comput Methods Appl Mech Eng 376:113609

    Article  MathSciNet  Google Scholar 

  • Abualigah L, Abd Elaziz M, Sumari P, Geem ZW, Gandomi AH (2022) Reptile Search Algorithm (RSA): a nature-inspired meta-heuristic optimizer. Expert Syst Appl 191:116158

    Article  Google Scholar 

  • Ammar EE, Khalifa HA (2019) Solving fully fuzzy multi-objective linear fractional programming problems based on fuzzy programming approach. J Fuzzy Math 27(2):301–312

    MATH  Google Scholar 

  • Anukokila P, Radhakrishnan B (2019) Goal programming approach to fully fuzzy fractional transportation problem J. Taibah Uni Sci 13(1):864–874

    Article  Google Scholar 

  • Anukokila P, Anju A, Radhakrishnan B (2017) Lexicographic approach for solving fully fuzzy fractional transportation problem. Int J Pure Appl Math 117(11):117–127

    Google Scholar 

  • Anukokila P, Radhakrishnan B, Anju A (2019) Goal programming approach for solving multi-objective fractional transportation problem with fuzzy parameters. RAIRO-Oper Res 53(1):157–178

    Article  MathSciNet  Google Scholar 

  • Arya R, Singh P, Kumari S, Obaidat MS (2020) An approach for solving fully fuzzy multi-objective linear fractional optimization problems. Soft Comput 24(12):9105–9119

    Article  Google Scholar 

  • Bajalinov EB (2003) Linear-fractional programming: Theory, methods, applications and software. Kluwer Academic Publishers, Boston

    Book  Google Scholar 

  • Bector CR, Chandra S (2005) Fuzzy mathematical programming and fuzzy matrix games. Springer, New York

  • Bharati SK (2019) Trapezoidal intuitionistic fuzzy fractional transportation problem. Soft Comp for problem solving (pp. 833–842). Springer, Singapore

  • Chakraborty M, Gupta S (2002) Fuzzy mathematical programming for multi-objective linear fractional programming problem. Fuzzy Sets Syst 125(3):335–342

    Article  MathSciNet  Google Scholar 

  • Charnes A, Cooper WW (1962) Programming with linear fractional functionals. Naval Res Logist Quart 9(3–4):181–186

    Article  MathSciNet  Google Scholar 

  • Das SK, Mandal T (2017) A MOLFP method for solving linear fractional programming under fuzzy environment. Int J Res Ind Eng 6(3):202–213

    Google Scholar 

  • Das SK, Mandal T, Edalatpanah SA (2015) A note on “A new method for solving fully fuzzy linear fractional programming with a triangular fuzzy numbers.” App Math Comp Intel 4(1):361–367

    Google Scholar 

  • Das SK, Mandal T, Edalatpanah SA (2017) A new approach for solving fully fuzzy linear fractional programming problems using the multi-objective linear programming. RAIRO-Oper Res 51(1):285–297

    Article  MathSciNet  Google Scholar 

  • Deb M, De PK (2015) Optimal solution of a fully fuzzy linear fractional programming problem by using graded mean integration representation method. Appl Appl Math 10(1):571–587

    MathSciNet  MATH  Google Scholar 

  • Deb M (2018) A study of fully fuzzy linear fractional programming problems by signed distance ranking technique. Optimization techniques for problem solving in uncertainty (pp. 73–115). IGI Global.

  • Ebrahimnejad A, Ghomi SJ, Mirhosseini-Alizamini SM (2017) A new approach for solving fully fuzzy linear fractional programming problems. IEEE 4th International Conference on Knowledge-Based Engineering and Innovation (pp. 0862–0865). IEEE, New York.

  • El Sayed MA, Abo-Sinna MA (2021) A novel approach for fully intuitionistic fuzzy multi-objective fractional transportation problem. Alex Eng J 60(1):1447–1463

    Article  Google Scholar 

  • Jadhav VA, Doke DM (2016) Solution procedure to solve fractional transportation problem with fuzzy cost and profit coefficients. Int J Math Comput Res 4(5):1554–1562

    Google Scholar 

  • Kacher Y, Singh P (2021) A comprehensive literature review on transportation problems. Int J Appl Comput Math 7(5):206

    Article  MathSciNet  Google Scholar 

  • Kalyani S, Maragatham L, Nagarani S (2016) An algorithm for linear fuzzy fractional transportation problem. Int J Eng Technol 4(10):61–68

    Google Scholar 

  • Kaur A, Kacprzyk J, Kumar A (2019) Fuzzy Transportation and Transshipment Problems. Springer Nature Switzerland AG, Switzerland

  • Kaur J, Kumar A (2017) A novel method for solving fully fuzzy linear fractional programming problems J. Intell Fuzzy Syst 33(4):1983–1990

    Article  Google Scholar 

  • Liu ST (2016) Fractional transportation problem with fuzzy parameters. Soft Comput 20(9):3629–3636

    Article  Google Scholar 

  • Loganathan T, Ganesan K (2019) A solution approach to fully fuzzy linear fractional programming problems. J Phys Conference Series 1377(1): 012040.

  • Loganathan T, Ganesan K (2021a) Solution of fully fuzzy linear fractional programming problem—a simple approach. IOP Conference Series: Mater Sci Eng 1130(1):012047

    Article  Google Scholar 

  • Loganathan T, Ganesan K (2021b) Fuzzy solution of fully fuzzy multi-objective linear fractional programming problems. Pak J Stat Oper Res 17(4):817–825

    Google Scholar 

  • Narayanamoorthy S, Kalyani S (2015) The intelligence of dual simplex method to solve linear fractional fuzzy transportation problem. Comput Intell Neurosci 1:103618

    Google Scholar 

  • Radhakrishnan B, Anukokila P (2014) A compensatory approach to fuzzy fractional transportation problem. Int J Math Oper Res 6(2):176–192

    Article  MathSciNet  Google Scholar 

  • Sheikhi A, Karbassi SM, Bidabadi N (2019) A novel algorithm for solving bi-objective fractional transportation problems with fuzzy numbers. J Math Ext 14(3):29–47

    MATH  Google Scholar 

  • Stanojevic B, Stancu-Minasian IM (2009) On solving fuzzified linear fractional programs. Adv Model Optim 11(4):503–523

    MathSciNet  Google Scholar 

  • Stanojević B, Stancu-Minasian IM (2012) Evaluating fuzzy inequalities and solving fully fuzzified linear fractional programs. Yugosl J Oper Res 22(1):41–50

    Article  MathSciNet  Google Scholar 

  • Stanojević B, Stanojević M (2014) Comment on “Fuzzy mathematical programming for multi objective linear fractional programming problem.” Fuzzy Sets Syst 246:156–159

    Article  MathSciNet  Google Scholar 

  • Swarup K (1966) Transportation technique in linear fractional functional programming. J R Naval Sci Serv 21(5):256–260

    Google Scholar 

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

    Article  MathSciNet  Google Scholar 

  • Zimmermann HJ (2001) Fuzzy set theory and its applications. Kluwer, Boston

    Book  Google Scholar 

Download references

Acknowledgements

The authors would like to thank to Associate Editor “Professor Raffaele CS Cerulli” and the anonymous reviewers for their valuable suggestions and comments which help in improving the quality of the paper.

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Authors and Affiliations

  1. School of Mathematics, Thapar Institute of Engineering & Technology (Deemed to Be University), Patiala, 147004, Punjab, India

    Tanveen Kaur Bhatia, Amit Kumar & Mahesh Kumar Sharma

Authors
  1. Tanveen Kaur Bhatia
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  2. Amit Kumar
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  3. Mahesh Kumar Sharma
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Correspondence to Amit Kumar.

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Bhatia, T.K., Kumar, A. & Sharma, M.K. Mehar approach to solve fuzzy linear fractional transportation problems. Soft Comput 26, 11525–11551 (2022). https://doi.org/10.1007/s00500-022-07408-x

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