Skip to main content
SpringerLink
Log in

Multi-objective fixed-charge solid transportation problem with product blending under intuitionistic fuzzy environment

  • Published:
Applied Intelligence Aims and scope Submit manuscript

Abstract

This paper analyzes multi-objective fixed-charge solid transportation problem with product blending in intuitionistic fuzzy environment. The parameters of multi-objective fixed-charge solid transportation problem may not be defined precisely because of globalization of the market and other unmanageable factors. So, we often hesitate in prediction of market demand and other parameters connected with transporting systems in a period. Based on these facts, the parameters of the formulated model are chosen as triangular intuitionistic fuzzy number. New ranking method is used to convert intuitionistic fuzzy multi-objective fixed-charge solid transportation problem with product blending to a deterministic form. New intuitionistic fuzzy technique for order preference by similarity to ideal solution (TOPSIS) is initiated to derive Pareto-optimal solution from the proposed model. Furthermore, we solve the formulated model using intuitionistic fuzzy programming; and a comparison is drawn between the obtained solutions extracted from the approaches. Finally, a practical (industrial) problem is incorporated to illustrate the applicability and feasibility of the proposed study. Conclusions with future research based on the paper are described at last.

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.

Fig. 1
Fig. 2

Similar content being viewed by others

References

  1. Abo-Sinna MA, Amer AH, Ibrahim AS (2008) Extension of TOPSIS for large scale multi-objective non-linear programming problems with block angular structure. Appl Math Model 32:292–302

    Article  MATH  Google Scholar 

  2. Aggarwal S, Gupta C (2016) Solving intuitionistic fuzzy solid transportation problem via new ranking method based on signed distance, International Journal of Uncertainty. Fuzziness Knowl-Based Syst 24:483–501

    Article  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  5. Boran FE, Gen S, Kurt M, Akay D (2009) A multi-criteria intuitionistic fuzzy group decision making for supplier selection with TOPSIS method. Expert Syst Appl 36:11363–11368

    Article  Google Scholar 

  6. Capuano N, Chiclana F, Fujita H, Viedma EH, Loia V (2018) Fuzzy group decision making with incomplete information guided by social influence. IEEE Trans Fuzzy Syst 26(3):1704– 1718

    Article  Google Scholar 

  7. Chen T, Tsao CY (2008) The interval-valued fuzzy TOPSIS method and experimental analysis. Fuzzy Sets Syst 159:1410–1428

    Article  MathSciNet  MATH  Google Scholar 

  8. Das A, Bera UK, Maiti M (2016) A breakable multi-item multi stage solid transportation problem under budget with Gaussian type-2 fuzzy parameters, Applied Intelligence. https://doi.org/10.1007/s10489-016-0794-y

  9. Das S, Guha D (2016) A centroid-based ranking method of trapezoidal intuitionistic fuzzy numbers and its application to MCDM problems. Fuzzy Inf Eng 8:41–74

    Article  MathSciNet  Google Scholar 

  10. Grzegrorzewski P (2003) The hamming distance between two intuitionistic fuzzy sets. In: proceedings of the 10th IFSA World Congress, Istanbul, pp s35–38

  11. Haley KB (1962) The solid transportation problen. Oper Res 10:448–463

    Article  MATH  Google Scholar 

  12. Hao Z, Xu Z, Zhao H, Fujita H (2018) A Dynamic weight determination approach based on the intuitionistic fuzzy bayesian network and its application to emergency decision making. IEEE Trans Fuzzy Syst 26 (4):1893–1907

    Article  Google Scholar 

  13. Hirsch WM, Dantzig GB (1968) The Fixed charge problem. Naval Res Logist Q 15:413–424

    Article  MathSciNet  MATH  Google Scholar 

  14. Hwang CL, Yoon K (1981) Multiple attribute decision making: Methods and Applications. Springer, New York

    Book  MATH  Google Scholar 

  15. Izadikhah M (2009) Using the Hamming distance to extend TOPSIS in a fuzzy environment. J Comput Appl Math 231:200–207

    Article  MathSciNet  MATH  Google Scholar 

  16. Jimenez F, Verdegay JL (1998) Uncertain solid transportation problems. Fuzzy Sets Syst 100:45–57

    Article  MathSciNet  Google Scholar 

  17. Kundu P, Kar S, Maiti M (2013) Multi-objective multi-item solid transportation problem in fuzzy environment. Appl Math Model 37:2028–2038

    Article  MathSciNet  MATH  Google Scholar 

  18. Kundu P, Kar MB, Kar S, Pal T, Maiti M (2017) A solid transportation model with product blending and parameters as rough variables. Soft Comput 21:2297–2306

    Article  MATH  Google Scholar 

  19. Li DF (2010) TOPSIS-Based nonlinear-programming methodology for multiattribute decision making with interval-valued intuitionistic fuzzy set. IEEE Trans Fuzzy Syst 18(2):299–311

    Google Scholar 

  20. Liao H, Si G, Xu Z, Fujita H (2018) Hesitant fuzzy linguistic preference utility set and its application in selection of fire rescue plans. Int J Environ Res Publ Health 15(4):664

    Article  Google Scholar 

  21. Li L, Lai KK (2000) A fuzzy approach to the multi-objective transportation problem. Comput Oper Res 27:43–57

    Article  MathSciNet  MATH  Google Scholar 

  22. Mahapatra DR, Roy SK, Biswal MP (2010) Multi-objective stochastic transportation problem involving log-normal. J Phys Sci 14:63–76

    MATH  Google Scholar 

  23. Maity G, Roy SK (2016) Solving a multi-objective transportation problem with nonlinear cost and multi-choice demand. Int J Manag Sci Eng Manag 11(1):62–70

    Google Scholar 

  24. Maity G, Roy SK, Verdegay JL (2016) Multi-objective transportation problem with cost reliability under uncertain environment. Int J Comput Intell Syst 9(5):839–849

    Article  Google Scholar 

  25. Maity G, Roy SK (2017) Multi-objective transportation problem using fuzzy decision variable through multi-choice programming. Int J Oper Res Inf Syst 8(3):82–96

    Article  Google Scholar 

  26. Majumder S, Kundu P, Kar S, Pal T (2018) Uncertain multi-objective multi-item fixed-charge solid transportation problem with budget constraint, Soft Computing, pp 1-23. https://doi.org/10.1007/s00500-017-2987-7

  27. Midya S, Roy SK (2014) Solving single-sink fixed-charge multi-objective multi-index stochastic transportation problem. Am J Math Manag Sci 33(4):300–314

    Google Scholar 

  28. Midya S, Roy SK (2017) Analysis of interval programming in different environments and its application to fixed-charge transportation problem, Discrete Mathematics. Algorithm Appl 9(3):1750040. 17 pages

    MATH  Google Scholar 

  29. Mitchell HB, Schaefer PA (2000) On ordering fuzzy numbers. Int J Intell Syst 15(11):981–993

    Article  MATH  Google Scholar 

  30. Nehi HM, Maleki HR (2005) Intuitionistic fuzzy numbers and its applications in fuzzy optimization problem. In: Proceedings of the 9th WSEAS international conference on systems, Athens, pp 1–5

  31. Papageorgiou DJ, Toriello A, Nemhauser GL, Savelsbergh MWP (2012) Fixed-charge transportation with product blending. Transp Sci 46(2):281–295

    Article  Google Scholar 

  32. Rani D, Gulati TR, Harish G (2016) Multi-objective non-linear programming problem in intuitionistic fuzzy environment: optimistic and pessimistic view point. Expert Syst Appl 64:228–238

    Article  Google Scholar 

  33. Roy SK, Ebrahimnejad A, Verdegay JL, Das S (2018) New approach for solving intuitionistic fuzzy multi-objective transportation problem. Sadhana 43(3):1–12. https://doi.org/10.1007/s12046-017-0777-7

  34. Roy SK, Maity G, Weber GW (2017) Multi-objective two-stage grey transportation problem using utility function with goals. CEJOR 25:417–439

    Article  MathSciNet  MATH  Google Scholar 

  35. Roy SK, Maity G (2017) Minimizing cost and time through single objective function in multi-choice interval valued transportation problem. J Intell Fuzzy Syst 32:1697–1709

    Article  MATH  Google Scholar 

  36. Roy SK, Maity G, Weber GW, Gök SZA (2017) Conic scalarization approach to solve multi-choice multi-objective transportation problem with interval goal. Ann Oper Res 253(1): 599–620

    Article  MathSciNet  MATH  Google Scholar 

  37. Roy SK, Midya S, Yu VF (2018) Multi-objective fixed-charge transportation problem with random rough variables, International Journal of Uncertainty. Fuzziness Knowl-Based Syst 26(6):971–996

    Article  Google Scholar 

  38. Sengupta D, Das A, Bera UK (2018) A gamma type-2 defuzzication method for solving a solid transportation problem considering carbon emission, Applied Intelligence. https://doi.org/10.1007/s10489-018-1173-7

  39. Singh SK, Yadav SP (2016) A new approach for solving intuitionistic fuzzy transportation problem of type-2. Ann Oper Res 243:349–363

    Article  MathSciNet  MATH  Google Scholar 

  40. Tian X, Xu Z, Fujita H (2018) Sequential funding the venture project or not? A prospect consensus process with probabilistic hesitant fuzzy preference information. Knowl-Based Syst 161:172–184

    Article  Google Scholar 

  41. Vahdani A, Mousavi SM, Moghaddam RT (2011) Group decision making based on novel fuzzy modified TOPSIS method. Appl Math Model 35:4257–4269

    Article  MathSciNet  MATH  Google Scholar 

  42. Varghese B, Kuriakose S (2016) Centroid of an intuitionistic fuzzy number. Notes Intuitionistic Fuzzy Sets 18(1):19–24

    MATH  Google Scholar 

  43. Wahed WFAE, Lee SM (2006) Interactive fuzzy goal programming for multi-objective transportation problems. Omega 34:158–166

    Article  Google Scholar 

  44. Wang JW, Cheng CH, Cheng HK (2009) Fuzzy hierarchical TOPSIS for supplier selection. Appl Soft Comput 9:377–386

    Article  Google Scholar 

  45. Zadeh LA (1965) Fuzzy Sets. Inf Control 8:338–353

    Article  MATH  Google Scholar 

  46. Zavardehi SMA, Nezhad SS, Moghaddam RT, Yazdani M (2013) Solving a fuzzy fixed charge solid transportation problen by metaheuristics. Fuzzy Sets Syst 57:183–194

    Google Scholar 

  47. Zhang B, Peng J, Li S, Chen L (2016) Fixed charge solid transportation problem in uncertain environment and its algorithm. Comput Ind Eng 102:186–197

    Article  Google Scholar 

  48. Zhou X, Wang L, Liao H, Wang S, Lev B, Fujita H (2019) A prospect theory-based group decision approach considering consensus for portfolio selection with hesitant fuzzy information. Knowl-Based Syst 168:28–38

    Article  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore, 721102, West Bengal, India

    Sankar Kumar Roy & Sudipta Midya

Authors
  1. Sankar Kumar Roy
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Sudipta Midya
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sankar Kumar Roy.

Ethics declarations

Conflict of interests

The authors have no conflict of interest for the publication of this paper.

Additional information

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

Roy, S.K., Midya, S. Multi-objective fixed-charge solid transportation problem with product blending under intuitionistic fuzzy environment. Appl Intell 49, 3524–3538 (2019). https://doi.org/10.1007/s10489-019-01466-9

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10489-019-01466-9

Keywords

Search

Navigation