Logo PTI Logo FedCSIS

Proceedings of the 17th Conference on Computer Science and Intelligence Systems

Annals of Computer Science and Information Systems, Volume 30

Intuitionistic Fuzzy Model of the Hungarian Algorithm for the Salesman Problem and Software Analysis of a Shipping Company Example

, ,

DOI: http://dx.doi.org/10.15439/2022F189

Citation: Proceedings of the 17th Conference on Computer Science and Intelligence Systems, M. Ganzha, L. Maciaszek, M. Paprzycki, D. Ślęzak (eds). ACSIS, Vol. 30, pages 383386 ()

Full text

Abstract. Here we propose for the first time a temporal intuitionistic fuzzy extension of the Hungarian method for solving the Travelling Salesman Problem (TIFHA-TSP) based on intuitionistic fuzzy logic and index matrices theories. The time for passing a given route between the settlements depends on different factors. The expert approach is used to determine the intuitionistic fuzzy time values for passing the routes between the settlements. The rating coefficients of the experts take the times into account. We are also developing an application for the algorithm's provision to use it on a real case of TIFHA-TSP.


  1. A. Mucherino, S. Fidanova, M. Ganzha, “Ant colony optimization with environment changes: An application to GPS surveying,” Proceedings of the 2015 FedCSIS, 2015, pp. 495 - 500.
  2. A. Sudha, G. Angel, M. Priyanka, S. Jennifer, “An Intuitionistic Fuzzy Approach for Solving Generalized Trapezoidal Travelling Salesman Problem,” International Journal of Mathematics Trends and Technology, vol. 29 (1), 2016, pp. 9-12.
  3. D. Mavrov, V. Atanassova, V. Bureva, O. Roeva, P. Vassilev, R. Tsvetkov, D. Zoteva, E. Sotirova, K. Atanassov, A. Alexandrov, H. Tsakov, “Application of Game Method for Modelling and Temporal Intuitionistic Fuzzy Pairs to the Forest Fire Spread in the Presence of Strong Wind,” Mathematics, vol. 10, 2022, 1pp. 1280. ttps://doi.org/10.3390/mat10081280
  4. D. Mavrov, “An Application for Performing Operations on Two-Dimensional Index Matrices,” Annual of “Informatics” Section, Union of Scientists in Bulgaria, vol. 10, 2019 / 2020, pp. 66-80.
  5. 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, vol. 222, 2009, pp. 7–19.
  6. H. Kuhn, The Travelling salesman problem, Proc. Sixth Symposium in Applied Mathematics of the American Mathematical Society, McGraw-Hill, New York; 1955
  7. J. Wong, “A new implementation of an algorithm for the optimal assignment problem: An improved version of Munkres’ algorithm,” BIT, vol. 19, 1979, pp. 418-424.
  8. K. Atanassov, On Intuitionistic Fuzzy Sets Theory, STUDFUZZ. Springer, Heidelberg, vol. 283; 2012. http://dx.doi.org/10.1007/978-3-642-29127-2.
  9. K. Atanassov, “Index Matrices: Towards an Augmented Matrix Calculus,” Studies in Computational Intelligence, Springer, vol. 573, 2014.
  10. K. Prabakaran, K. Ganesan, “Fuzzy Hungarian method for solving intuitionistic fuzzy travelling salesman problem,” Journal of Physics: Conf. Series, vol. 1000, 2018, pp. 2-13.
  11. L. Biggs, K. Lloyd, R. Wilson, Graph Theory 1736-1936, Clarendon Press, Oxford; 1986.
  12. L. Zadeh, “Fuzzy Sets,” Information and Control, vol. 8 (3), 1965, pp. 338-353.
  13. S. Akshitha, K. S. Ananda Kumar, M. Nethrithameda, R. Sowmva, and R. Suman Pawar, “Implementation of hungarian algorithm to obtain optimal solution for travelling salesman problem,” 2018, pp. 2470–2474.
  14. S. Dhanasekar, S. Hariharan, P. Sekar, “Classical travelling salesman problem based approach to solve fuzzy TSP using Yager’s Ranking,” Int. Journal of Computer Applications, vol. 74 (13), 2013, pp. 1-4.
  15. S. Dhanasekar, V. Parthiban, D. Gururaj, “Improved Hungarian method to solve fuzzy assignment problem and fuzzy TSP,” Advances in Mathematics: Scientific Journal, vol. 9 (11), 2021, pp. 9417-9427.
  16. 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.
  17. 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.
  18. V. Traneva, S. Tranev, Index Matrices as a Tool for Managerial Decision Making, Publ. House of the USB; 2017 (in Bulgarian).
  19. V. Traneva, S. Tranev, “An Intuitionistic Fuzzy Approach to the Travelling Salesman Problem,” In: Lirkov, I., Margenov, S. (eds) Large-Scale Scientific Computing, LSSC 2019, Lecture Notes in Computer Science, vol. 11958. Springer, Cham, 2021, pp. 530-539.