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Polish Information Processing Society
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Annals of Computer Science and Information Systems, Volume 21

Proceedings of the 2020 Federated Conference on Computer Science and Information Systems

Intuitionistic Fuzzy Transportation Problem by Zero Point Method


DOI: http://dx.doi.org/10.15439/2020F61

Citation: Proceedings of the 2020 Federated Conference on Computer Science and Information Systems, M. Ganzha, L. Maciaszek, M. Paprzycki (eds). ACSIS, Vol. 21, pages 349358 ()

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Abstract. The transportation problems (TPs) support the optimal management of the transport deliveries. In classical TPs the decision maker has information about the crisp values of the transportation costs, availability and demand of the products. Sometimes in the parameters of TPs in real life there is ambiguity and vagueness caused by uncontrollable market factors.


  1. A. Edwuard Samuel, “Improved zero point method,” Applied mathemat ical sciences, vol. 6 (109), 2012, pp. 5421–5426.
  2. A. Edwuard Samuel, M. Venkatachalapathy, “Improved zero point method for unbalanced FTPs,” International Journal of Pure and Applied Mathematics, vol. 94 (3), 2014, pp. 419–424.
  3. A. Gani, A. Samuel, D. Anuradha, “Simplex type algorithm for solving fuzzy transportation problem,” Tamsui Oxf. J. Inf. Math. Sci., vol. 27, 2011, pp. 89–98.
  4. A. Gani, S. Abbas, “A new average method for solving intuitionistic fuzzy transportation problem,” International Journal of Pure and Applied Mathematics, vol. 93 (4), 2014, pp. 491-499.
  5. A. Kaur, A. Kumar, “A new approach for solving fuzzy transportation problems using generalized trapezoidal fuzzy numbers,” Applied Soft Computing, vol. 12 (3), 2012, pp. 1201-1213.
  6. A. Kaur, J. Kacprzyk and A. Kumar, Fuzzy transportation and transshipment problems, Studies in fuziness and soft computing, vol. 385, 2020.
  7. A. Patil, S. Chandgude, “Fuzzy Hungarian Approach for Transportation Model,” International Journal of Mechanical and Industrial Engineer ing, vol. 2 (1), pp. 77-80, 2012.
  8. B. Atanassov, Quantitative methods in business management, Publ. houseTedIna, Varna; 1994. (in Bulgarian)
  9. D. Dinagar, K. Palanivel, “On trapezoidal membership functions in solving transportation problem under fuzzy environment,” Int. J. Comput. Phys. Sci., vol. 1, 2009, pp. 1–12.
  10. E. Szmidt, J. Kacprzyk, “Amount of information and its reliability in the ranking of Atanassov’s intuitionistic fuzzy alternatives,” in: Rakus-Andersson, E., Yager, R., Ichalkaranje, N., Jain, L.C. (eds.), Recent Advances in Decision Making, SCI, Springer, Heidelberg, vol. 222, http://dx.doi.org/10.1007/978-3-642-02187-9_2, 2009, pp. 7–19.
  11. F. Jimenez, J. Verdegay, “Solving fuzzy solid transportation problems by an evolutionary algorithm based parametric approach,” European Journal of Operational Research, vol. 117 (3),1999, pp. 485-510.
  12. F. Hitchcock, “The distribution of a product from several sources to numerous localities,” Journal of Mathematical Physics, vol. 20, 1941, pp. 224-230.
  13. G. Dantzig, Application of the simplex method to a transportation problem, Chapter XXIII, Activity analysis of production and allocation, New York, Wiley, Cowles Commision Monograph, vol. 13, 359-373; 1951.
  14. G. Gupta, A. Kumar, M. Sharma, “A Note on A New Method for Solving Fuzzy Linear Programming Problems Based on the Fuzzy Linear Complementary Problem (FLCP),” International Journal of Fuzzy Systems, 2016, pp. 1-5.
  15. H. Arsham, A. Khan, “A simplex type algorithm for general transportation problems-An alternative to stepping stone,” Journal of Operational Research Society, vol. 40 (6), 2017, pp. 581-590.
  16. H. Basirzadeh, “An approach for solving fuzzy transportation problem, ” Appl. Math. Sci., vol. 5, 2011, pp. 1549–1566.
  17. K. Atanassov, “Intuitionistic Fuzzy Sets,” VII ITKR Session, Sofia, 20-23 June 1983 (Deposed in Centr. Sci.-Techn. Library of the Bulg. Acad. of Sci., 1697/84) (in Bulgarian). Reprinted: Int. J. Bioautomation, vol. 20(S1), 2016, pp. S1-S6.
  18. K. Atanassov, “Generalized index matrices,” Comptes rendus de l’Academie Bulgare des Sciences, vol. 40(11), 1987, pp. 15-18.
  19. K. Atanassov, On Intuitionistic Fuzzy Sets Theory, STUDFUZZ. Springer, Heidelberg, vol. 283; http://dx.doi.org/10.1007/978-3-642-29127-2, 2012.
  20. K. Atanassov, Index Matrices: Towards an Augmented Matrix Calculus. Studies in Computational Intelligence, Springer, Cham, vol. 573; http://dx.doi.org/10.1007/978-3-319-10945-9, 2014.
  21. K. Atanassov, “Intuitionistic Fuzzy Logics,” Studies in Fuzziness and Soft Computing, Springer, vol. 351, http://dx.doi.org/10.1007/978-3-319-48953-7, 2017.
  22. K. Atanassov, “n-Dimensional extended index matrices Part 1,” Advanced Studies in Contemporary Mathematics, vol. 28 (2), 2018, pp. 245-259.
  23. K. Atanassov, E. Szmidt, J. Kacprzyk, “On intuitionistic fuzzy pairs,” Notes on Intuitionistic Fuzzy Sets, vol. 19 (3), 2013, pp. 1-13.
  24. K. Kathirvel, K. Balamurugan, “Method for solving fuzzy transportation problem using trapezoidal fuzzy numbers,” International Journal of Engineering Research and Applications, vol. 2 (5), 2012, pp. 2154-2158.
  25. K. Kathirvel, K. Balamurugan, “Method for solving unbalanced transportation problems using trapezoidal fuzzy numbers,” International Journal of Engineering Research and Applications, vol. 3 ( 4), 2013, pp. 2591-2596.
  26. L. Kantorovich, M. Gavyrin, Application of mathematical methods in the analysis of cargo flows, Coll. of articles Problems of increasing the efficiency of transport, M.: Publ. house AHSSSR, 110-138; 1949. (in Russian)
  27. L. Zadeh, Fuzzy Sets, Information and Control, vol. 8 (3), 338-353; 1965.
  28. M. Gen, K. Ida, Y. Li, E. Kubota, “Solving bicriteria solid transportation problem with fuzzy numbers by a genetic algorithm,” Computers & Industrial Engineering, vol. 29 (1), 1995, pp. 537-541.
  29. M. Purushothkumar, M. Ananthanarayanan, S. Dhanasekar, “Fuzzy zero suffix Algorithm to solve Fully Fuzzy Transportation Problems,” International Journal of Pure and Applied Mathematics, vol. 119 (9), 2018, pp. 79-88.
  30. M. Shanmugasundari, K. Ganesan, “A novel approach for the fuzzy optimal solution of fuzzy transportation problem,” International journal of Engineering research and applications, vol. 3 (1), 2013, pp. 1416-1424.
  31. N. Lalova, L. Ilieva, S. Borisova, L. Lukov, V. Mirianov, A guide to mathematical programming, Science and Art Publishing House, Sofia; 1980 (in Bulgarian)
  32. P. Jayaraman, R. Jahirhussain, “Fuzzy optimal transportation problem by improved zero suffix method via Robust Ranking technique,” International Journal of Fuzzy Mathematics and systems, vol. 3 (4), 2013, pp. 303-311.
  33. P. Kumar, R. Hussain, “A method for solving unbalanced intuitionistic fuzzy transportation problems,” Notes on Intuitionistic Fuzzy Sets, vol. 21 (3), 2015, pp. 54-65.
  34. P. Ngastiti, B. Surarso, B. Sutimin, “Zero point and zero suffix methods with robust ranking for solving fully fuzzy transportation problems,” Journal of Physics: Conference Series, vol. 1022, 2018, pp. 1-10.
  35. P. Pandian, G. Natarajan, “A new algorithm for finding a fuzzy optimal solution for fuzzy transportation problems,” Applied Mathematical Sciences, vol. 4, 2010, pp. 79-90.
  36. R. Antony, S. Savarimuthu, T. Pathinathan, “Method for solving the transportation problem using triangular intuitionistic fuzzy number,” International Journal of Computing Algorithm, vol. 03, 2014, pp. 590-605.
  37. R. Jahirhussain, P. Jayaraman, “Fuzzy optimal transportation problem by improved zero suffix method via robust rank techniques,” International Journal of Fuzzy Mathematics and Systems (IJFMS), vol. 3, 2013, pp. 303-311.
  38. R. Jahihussain , P. Jayaraman, “A new method for obtaining an optinal solution for fuzzy transportation problems,” International Journal of Mathematical Archive, vol. 4 (11), 2013, pp. 256-263.
  39. S. Chanas, W. Kolodziejckzy, A. Machaj, “A fuzzy approach to the transportation problem,” Fuzzy Sets and Systems, vol. 13, 1984, pp. 211-221.
  40. S. Dhanasekar, S. Hariharan, P. Sekar, “Fuzzy Hungarian MODI Algorithm to solve fully fuzzy transportation problems,” Int. J. Fuzzy Syst., vol. 19 (5), 2017, pp. 1479-1491.
  41. S. Liu, C. Kao, “Solving fuzzy transportation problems based on extension principle,” Eur. J. Oper. Res., vol. 153, 2004, pp. 661–674.
  42. S. Mohideen, P. Kumar, “A Comparative Study on Transportation Problem in Fuzzy Environment,” International Journal of Mathematics Research, vol. 2 (1), 2010, pp. 151-158.
  43. T. Karthy, K. Ganesan, “Revised improved zero point method for the trapezoidal fuzzy transportation problems,” AIP Conference Proceedings, 2112, 020063, 2019, pp. 1-8.
  44. V. Sudhagar, V. Navaneethakumar, “Solving the Multiobjective two stage fuzzy transportation problem by zero suffix method,” Journal of Mathematics Research,vol. 2 (4), 2010, pp. 135-140.
  45. V. Traneva, “Internal operations over 3-dimensional extended index matrices,” Proceedings of the Jangjeon Mathematical Society, vol. 18 (4), 2015, pp. 547-569.
  46. V. Traneva, S. Tranev, V. Atanassova, “An Intuitionistic Fuzzy Approach to the Hungarian Algorithm,” in: G. Nikolov et al. (Eds.): NMA 2018, LNCS 11189, Springer Nature Switzerland, AG, 2019, pp. 1–9, http://dx.doi.org/10.1007/978-3-030-10692-8_19.
  47. V. Traneva, S. Tranev, M. Stoenchev, K. Atanassov, “ Scaled aggregation operations over two- and three-dimensional index matrices,” Soft computing, vol. 22, 2019, pp. 5115-5120, http://dx.doi.org/10.1007/s00500-018-3315-6.
  48. V. Traneva, S. Tranev, Index Matrices as a Tool for Managerial Decision Making, Publ. House of the Union of Scientists, Bulgaria; 2017 (in Bulgarian)
  49. V. Traneva, S. Tranev, “An Intuitionistic fuzzy zero suffix method for solving the transportation problem,” in: Dimov I., Fidanova S. (eds) Advances in High Performance Computing. HPC 2019, Studies in computational intelligence, Springer, Cham, vol. 902, http://dx.doi.org/10.1007/978-3-030-55347-0_7, 2020.