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Intuitionistic Fuzzy Hamiltonian Cycle by Index Matrices

Wybrane pełne teksty z tego czasopisma
Identyfikatory
Warianty tytułu
Konferencja
Federated Conference on Computer Science and Information Systems (15 ; 06-09.09.2020 ; Sofia, Bulgaria)
Języki publikacji
EN
Abstrakty
EN
In this paper, the algorithm for finding a Hamiltonian cycle in an intuitionistic fuzzy graph (IFG) is proposed, based on the theories of intuitionistic fuzzy sets (IFSs) and of index matrices (IMs). The aim of the paper is to extend the algorithm to find a fuzzy Hamiltonian cycle (FHC) in an IFG to the intuitionistic fuzzy (IFHC) using the IFSs and IMs concepts. An intuitionistic fuzzy graph example about network of Wizz air airlines is modeled by the extended IM to illustrate the proposed algorithm. In the paper also are introduced for the first time three index-type operations over IMs.
Rocznik
Tom
Strony
345--348
Opis fizyczny
Bibliogr. 28 poz., wz., rys.
Twórcy
  • “Prof. Asen Zlatarov" University “Prof. Yakimov" Blvd, Burgas 8000, Bulgaria
  • “Prof. Asen Zlatarov" University “Prof. Yakimov" Blvd, Burgas 8000, Bulgaria
Bibliografia
  • 1. A. Gani, S. Latha, “A new algorithm to find fuzzy Hamilton cycle in a fuzzy network using adjacency matrix and minimum vertex degree,” SpringerPlus, International Journal of Pure and Applied Mathematics, vol. 5, 2016, 1854.
  • 2. A. Kauffman, Introduction a la Theorie des Sous-emsembles Flous, Paris: Masson et Cie Editeurs, 1973.
  • 3. A. Rosenfeld, “Fuzzy graphs,” in: L.A. Zadeh, K.S. Fu, M. Shimura (Eds.), Fuzzy Sets and Their Applications, Academic Press, New York, 1975, pp. 77–95.
  • 4. A. Shannon, K. Atanassov, “A first step to a theory of the intuitionistic fuzzy graph,” in D. lakov, ed., Proc. of the First workshop on Fuzzy based expert systems, Sofia, 1994, pp. 59-61.
  • 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, Heidelberg, vol. 222, 2009, pp. 7–19.
  • 6. GA. Dirac, “Some theorems on abstract graphs,” Proc Lond Math Soc, vol. 3 (1), 1952, pp. 69–81.
  • 7. G. Fan, “New sufficient conditions for cycles in graphs,” J Comb Theory Ser B, vol. 37, 1984, pp. 221–227.
  • 8. JN. Mordeson, PS. Nai, “Cycles and co-cycles of fuzzy graphs,” Inf Sci, vol. 90, 1996, pp. 39–49.
  • 9. K. Atanassov, “Intuitionistic Fuzzy Sets,” VII ITKR Session, Sofia, 20-23 June 1983.
  • 10. K. Atanassov, “Generalized index matrices,” Comptes rendus de l’Academie Bulgare des Sciences, vol. 40(11), 1987, pp. 15-18.
  • 11. K. Atanassov, On Intuitionistic Fuzzy Sets Theory, STUDFUZZ. Springer, Heidelberg, vol. 283; 2012.
  • 12. K. Atanassov, Index Matrices: Towards an Augmented Matrix Calculus. Studies in Computational Intelligence, Springer, Cham, vol. 573; 2014.
  • 13. K. Atanassov, “n-Dimensional extended IMs Part 1,” Advanced Studies in Contemporary Mathematics, vol. 28 (2), 2018, pp. 245-259.
  • 14. K. Atanassov, Interval-valued intuitionistic fuzzy sets, Studies in Fuzziness and Soft Computing, vol. 388; 2020.
  • 15. K. Atanassov, E. Szmidt, J. Kacprzyk, “On intuitionistic fuzzy pairs,” Notes on Intuitionistic Fuzzy Sets, vol. 19 (3), 2013, pp. 1-13.
  • 16. 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.
  • 17. K. Zhao, Lai Hong-Jian, Shao Yehang, “New sufficient condition for Hamiltonian graphs,” Appl Math Lett, vol. 20, 2007, 116–122.
  • 18. L. Zadeh, Fuzzy Sets, Information and Control, vol. 8 (3), 338-353; 1965.
  • 19. O. Ore, “Note on Hamiltonian circuits.” Am Math Mon, vol. 67, 1960, pp. 55.
  • 20. RM. Karp, “Reducibility among combinatorial problems,” in: Miller RE, Thatcher JW (eds), Complexity of computations, Plemem Press, New York, 1972, pp. 85–103.
  • 21. S. Skiena, Hamiltonian cycles. Implementing discrete mathematics: combinatorics and graph theory with mathematica reading, Addison Wesley, New York; 1990, pp 196–198.
  • 22. V. Andonov, “On some properties of one Cartesian product over Intuitionistic fuzzy sets." Notes on Intuitionistic Fuzzy Sets, vol. 14 (1), 2008,12–19.
  • 23. V. Chvatal, “On Hamilton’s ideals,” J Combin Theory Ser B, vol. 12, 1972, pp. 63–168.
  • 24. V. Traneva, “Internal operations over 3-dimensional extended index matrices,” Proceedings of the Jangjeon Mathematical Society, vol. 18 (4), 2015, pp. 547-569.
  • 25. 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.
  • 26. 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.
  • 27. V. Traneva, S. Tranev, Index Matrices as a Tool for Managerial Decision Making, Publ. House of the Union of Scientists, Bulgaria; 2017
  • 28. http://wizz.air-bg.com, last accessed 29 june 2020.
Uwagi
1. Track 1: Artificial Intelligence
2. Technical Session: 13th International Workshop on Computational Optimization
3. Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2021).
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-2140b2f6-ffc3-48a7-b105-e4df2d7a232a
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