Approximate Membership Function Shapes of Solutions to Intuitionistic Fuzzy Transportation Problems

Authors

  • Bogdana Stanojevic Math. Inst. of the Serbian Academy of Sciences and Arts
  • Milan Stanojević

Keywords:

full fuzzy transportation problem, extension principle, intuitionistic fuzzy numbers

Abstract

In this paper, proposing a mathematical model with disjunctive constraint system, and providing approximate membership function shapes to the optimal values of the decision variables, we improve the solution approach to transportation problems with trapezoidal fuzzy parameters. We further extend the approach to solving transportation problems with intuitionistic fuzzy parameters; and compare the membership function shapes of the fuzzy solutions obtained by our approach to the fuzzy solutions to full fuzzy transportation problems yielded by approaches found in the literature.

Author Biography

Bogdana Stanojevic, Math. Inst. of the Serbian Academy of Sciences and Arts

Applied Mathematics, associate researcher

References

[1] Anukokila, P.; Radhakrishnan, B. (2019). Goal programming approach to fully fuzzy fractional transportation problem. Journal of Taibah University for Science, 13(1), 864-874, 2019. https://doi.org/10.1080/16583655.2019.1651520

[2] Atanassov, K.T. (1986). Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20(1), 87-96, 1986. https://doi.org/10.1016/S0165-0114(86)80034-3

[3] Bellman, R.E.; Zadeh, L.A. (1970). Decision-making in a fuzzy environment. Management Science, 17(4), B-141-B-164, 1970. https://doi.org/10.1287/mnsc.17.4.B141

[4] Dzitac, I.; Filip, F.G.; Manolescu, M.J. (2017). Fuzzy logic is not fuzzy: World-renowned computer scientist Lotfi A. Zadeh, International Journal of Computers Communications & Control, 12(6), 748-789, 2017. https://doi.org/10.15837/ijccc.2017.6.3111

[5] Ebrahimnejad, A.; Verdegay, J.L. (2018). A new approach for solving fully intuitionistic fuzzy transportation problems. Fuzzy Optim Decis Making, 17, 447-474, 2018. https://doi.org/10.1007/s10700-017-9280-1

[6] Ghanbari, R.; Ghorbani-Moghadam, K,; Mahdavi-Amiri, N.; De Baets, B. (2020). Fuzzy linear programming problems: models and solutions. Soft Computing, 24, 10043-10073, 2020. https://doi.org/10.1007/s00500-019-04519-w

[7] Kumar, A.; Kaur, A. (2012). Methods for solving unbalanced fuzzy transportation problems. Int. J. Operational Research, 12, 287-316, 2012. https://doi.org/10.1007/s12351-010-0101-3

[8] Kumar, P.S.; Hussain, R.J. (2016). Computationally simple approach for solving fully intuitionistic fuzzy real life transportation problems. Int J Syst Assur Eng Manag, 7, 90-101, 2016. https://doi.org/10.1007/s13198-014-0334-2

[9] Liu, S.-T. (2016). Fractional transportation problem with fuzzy parameters. Soft Computing, 20, 3629-3636, 2016. https://doi.org/10.1007/s00500-015-1722-5

[10] Liu, S.-T.; Kao, C. (2004). Solving fuzzy transportation problems based on extension principle. European Journal of Operational Research, 153(3), 661-674, 2004. https://doi.org/10.1016/S0377-2217(02)00731-2

[11] Mahmoodirad, A.; Allahviranloo, T.; Niroomand, S. (2019). A new effective solution method for fully intuitionistic fuzzy transportation problem. Soft Computing, 23, 4521-4530, 2019. https://doi.org/10.1007/s00500-018-3115-z

[12] Mishra, A.; Kumar, A. (2020). Jmd method for transforming an unbalanced fully intuitionistic fuzzy transportation problem into a balanced fully intuitionistic fuzzy transportation problem. Soft Computing, 24, 15639-15654, 2020. https://doi.org/10.1007/s00500-020-04889-6

[13] Singh, S.K.; Yadav, S.P. (2016). A novel approach for solving fully intuitionistic fuzzy transportation problem. Int. J. Operational Research, 2, 460-472, 2016. https://doi.org/10.1504/IJOR.2016.077684

[14] Stanojevic, B.; Dzitac, S.; Dzitac, I. (2020). Fuzzy numbers and fractional programming in making decisions. International Journal of Information Technology & Decision Making, 19(4), 1123-1147, 2020. https://doi.org/10.1142/S0219622020300037

[15] Stanojevic, B.; Stanojevic, M. (2020). Solution value envelope to full fuzzy transportation problems. In: D. Starcevic, S. Marinkovic (eds), Bussiness and Artificial Intelligence, Proceedings of SymOrg 2020, Belgrade, Serbia, 319-326, 2020.

[16] Stanojevic, B.; Stanojevic, M. (2021). Empirical versus analytical solutions to full fuzzy linear programming. In: Dzitac, I., Dzitac, S., Filip, F.G., Kacprzyk, J., Manolescu, M.J., Oros, H. (eds) Intelligent Methods in Computing, Communications and Control. ICCCC 2020. Advances in Intelligent Systems and Computing, vol 1243, Springer, Cham, 220-233, 2021. https://doi.org/10.1007/978-3-030-53651-0_19

[17] Zadeh, L.A. (1965). Fuzzy sets. Information and Control, 8(3), 338-353, 1965. https://doi.org/10.1016/S0019-9958(65)90241-X

[18] Zadeh, L.A. (1975). The concept of a linguistic variable and its application to approximate reasoning I. Information Sciences, 8(3), 199-249, 1975. https://doi.org/10.1016/0020-0255(75)90036-5

[19] Zimmermann, H.-J. (1978). Fuzzy programming and linear programming with several objective functions. Fuzzy Sets and Systems, 1(1), 45-55, 1978. https://doi.org/10.1016/0165-0114(78)90031-3

[20] Zimmermann, H.-J. (1985). Applications of fuzzy set theory to mathematical programming. Information Sciences, 36(1), 29-58, 1985. https://doi.org/10.1016/0020-0255(85)90025-8

Additional Files

Published

2020-10-08

Most read articles by the same author(s)

Obs.: This plugin requires at least one statistics/report plugin to be enabled. If your statistics plugins provide more than one metric then please also select a main metric on the admin's site settings page and/or on the journal manager's settings pages.