[go: up one dir, main page]
More Web Proxy on the site http://driver.im/
Logo PTI Logo FedCSIS

Position and Communication Papers of the 16th Conference on Computer Science and Intelligence Systems

Annals of Computer Science and Information Systems, Volume 26

Two-Stage Intuitionistic Fuzzy Transportation Problem through the Prism of Index Matrices

,

DOI: http://dx.doi.org/10.15439/2021F76

Citation: Position and Communication Papers of the 16th Conference on Computer Science and Intelligence Systems, M. Ganzha, L. Maciaszek, M. Paprzycki, D. Ślęzak (eds). ACSIS, Vol. 26, pages 8996 ()

Full text

Abstract. In today's market environment not all the parameters of the transportation problems may not be known precisely. Uncertain data can be represented by fuzzy sets (FSs). Intuitionistic FSs (IFSs) are an extension of FSs with a degree of hesitansy. The paper presents a new approach for solution of a two-stage intuitionistic fuzzy transportation problem (2-S IFTP) through the prism of index matrices (IMs). Its main objective is to find the quantities of delivery from manifacturers and resselers to buyers to maintain the supply and demand requirements at the cheapest transportation costs. The solution procedure is demonstrated by a numerical example.

References

  1. A. Edwuard Samuel, “Improved zero point method,” Applied mathematical sciences, vol. 6 (109), 2012, pp. 5421–5426.
  2. 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.
  3. A. Gani, K. Razak, “Two stage fuzzy transportation problem,” J Phys Sci, vol. 10, 2006, pp. 63–69.
  4. A. Gani, S. Abbas, “A new average method for solving intuitionistic fuzzy transportation problem,” International Journal of Pure and Ap- plied 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 Engineering, vol. 2 (1), pp. 77-80, 2012.
  8. A.E. Samuel, M. Venkatachalapathy, “Modified vogel’s approximation method for fuzzy transportation problems,” Appl. Math. Sci., vol. 5, 2011, pp. 1367–1372.
  9. B. Atanassov, Quantitative methods in business management, Publ. houseTedIna, Varna; 1994. (in Bulgarian)
  10. B. Riecan, A. Atanassov, “Operation division by n over intuitionistic fuzzy sets,” NIFS, vol. 16, No. 4, 2010, pp. 1-4.
  11. S. Dinagar, K. Palanivel, “The transportation problem in fuzzy environment,” Int. J. Algorithms Comput. Math., vol. 2, 2009, pp. 65–71.
  12. 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, 2009, pp. 7–19.
  13. 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.
  14. F. Hitchcock, “The distribution of a product from several sources to numerous localities,” Journal of Mathematical Physics, vol. 20, 1941, pp. 224-230.
  15. 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.
  16. 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.
  17. H. Basirzadeh, “An approach for solving fuzzy transportation problem, ” Appl. Math. Sci., vol. 5, 2011, pp. 1549–1566.
  18. 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.
  19. K. Atanassov, “Generalized index matrices,” Comptes rendus de l’Academie Bulgare des Sciences, vol. 40(11), 1987, pp. 15-18.
  20. K. Atanassov, On Intuitionistic Fuzzy Sets Theory, STUDFUZZ. Springer, Heidelberg, vol. 283; http://dx.doi.org/10.1007/978-3-642-29127-2, 2012.
  21. 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.
  22. 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.
  23. K. Atanassov, “n-Dimensional extended index matrices Part 1,” Advanced Studies in Contemporary Mathematics, vol. 28 (2), 2018, pp. 245-259.
  24. K. Atanassov, “Remark on an intuitionistic fuzzy operation division,” Annual of Informatics Section, Union of Scientists in Bulgaria, vol. 10, 2019 (in press)
  25. K. Atanassov, G. Gargov, “Interval valued intuitionistic fuzzy sets,” Fuzzy sets and systems, vol. 31 (3), 1989, pp. 343-349.
  26. K. Atanassov, E. Szmidt, J. Kacprzyk, “On intuitionistic fuzzy pairs,” Notes on Intuitionistic Fuzzy Sets, vol. 19 (3), 2013, pp. 1-13.
  27. 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.
  28. 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.
  29. L. Zadeh, Fuzzy Sets, Information and Control, vol. 8 (3), 338-353; 1965.
  30. 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.
  31. 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.
  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. Kaur, K. Dahiya, “Two-stage interval time minimization transportation problem with capacity constraints,” Innov Syst Des Eng, vol. 6, 2015, pp.79–85.
  34. 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.
  35. 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.
  36. 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.
  37. 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.
  38. S. K. Bharati, R. Malhotra, “Two stage intuitionistic fuzzy time minimizing TP based on generalized Zadeh’s extension principle,” Int J Syst Assur Eng Manag, vol. 8, 2017, pp. 1142-1449. http://dx.doi.org/10.1007/s13198-017-0613-9
  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. Midya, SS. K. Roy, V. F. Yu, “Intuitionistic fuzzy multi-stage multi-objective fixed-charge solid transportation problem in a green supply chain,” Int. J. Mach. Learn. & Cyber., vol. 12, 2021, pp. 699–717.
  43. S. Malhotra, R. Malhotra, “A polynomial Algorithm for a Two – Stage Time Minimizing Transportation Problem, OPSEARCH, vol. 39, 2002, pp. 251–266.
  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, “One application of the index matrices for a solution of a transportation problem,” Advanced Studies in Contemporary Mathematics, vol. 26 (4), 2016, pp. 703-715.
  47. V. Traneva, P. Marinov, K. Atanassov, “Index matrix interpretations of a new transportation-type problem,” Comptes rendus de l’Academie Bulgare des Sciences, vol. 69 (10), 2016, pp. 1275-1283.
  48. V. Traneva, S. Tranev, “Intuitionistic Fuzzy Transportation Problem by Zero Point Method,” Proceedings of the 15th Conference on Computer Science and Information Systems (FedCSIS), Sofia, Bulgaria, 2020, pp. 345–348. http://dx.doi.org/10.15439/2020F61
  49. 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
  50. 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
  51. V. Traneva, S. Tranev, Index Matrices as a Tool for Managerial Decision Making, Publ. House of the Union of Scientists, Bulgaria; 2017 (in Bulgarian).
  52. 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