Abstract
In this paper, an algorithm for searching the minimum spanning tree (MST) in a network having trapezoidal fuzzy neutrosophic edge weight is presented. The network is an undirected neutrosophic weighted connected graph (UNWCG). The proposed algorithm is based on matrix approach to design the MST of UNWCG. A numerical example is provided to check the validity of the proposed algorithm. Next, a comparison example is made with Mullai’s algorithm in neutrosophic graphs.
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References
Smarandache, F.: Neutrosophy. Neutrosophic probability, set, and logic. In: ProQuest Information & Learning, Ann Arbor, Michigan, USA (1998)
Wang, H., Smarandache, F., Zhang,Y., Sunderraman, R.: Single valued neutrosophic sets. In: Multisspace and Multistructure, vol. 4, pp. 410–413 (2010)
Kandasamy, I.: Double-valued neutrosophic sets, their minimum spanning trees, and clustering algorithm. J. Intell. Syst. 1–17 (2016). https://doi.org/10.1515/jisys-2016-0088
Ye, J.: Single valued neutrosophic minimum spanning tree and its clustering method. J. Intell. Syst. 23, 311–324 (2014)
Mandal, K., Basu, K.: Improved similarity measure in neutrosophic environment and its application in finding minimum spanning tree. J. Intell. Fuzzy Syst. 31, 1721–1730 (2016)
Broumi, S., Bakali, A., Talea, M., Smarandache, F., Kishore Kumar, P.K.: Shortest path problem on single valued neutrosophic graphs. In: 2017 International Symposium on Networks, Computers and Communications (ISNCC) (2017). (in press)
Broumi, S., Talea, M., Bakali, A., Smarandache, F.: Single valued neutrosophic graphs. J. New Theory N 10, 86–101 (2016)
Broumi, S., Talea, M., Smarandache, F., Bakali, A.: Single valued neutrosophic graphs: degree, order and size. In: IEEE International Conference on Fuzzy Systems (FUZZ), pp. 2444–2451 (2016)
Broumi, S., Smarandache, F., Talea, M., Bakali, A.: Decision-making method based on the interval valued neutrosophic graph. In: Future Technologie, pp. 44–50. IEEE (2016)
Mullai, M., Broumi, S., Stephen, A.: Shortest path problem by minimal spanning tree algorithm using bipolar neutrosophic numbers. Int. J. Math. Trends Technol. 46(N2), 80–87 (2017)
Ye, J.: Trapezoidal fuzzy neutrosophic set and its application to multiple attribute decision making. In: Neural Computing and Applications (2014). https://doi.org/10.1007/s00521-014-1787-6
Zhang, C., Li, D., Sangaiah, A.K., Broumi, S.: Merger and acquisition target selection based on interval neutrosophic multigranulation rough sets over two universes. In: Symmetry, vol. 9, no. 7, p. 126 (2017). https://doi.org/10.3390/sym9070126
Abdel-Basset, M., Mohamed, M., Sangaiah, A.K.: Neutrosophic AHP-delphi group decision making model based on trapezoidal neutrosophic numbers. J. Ambient Intell. Hum. Comput. 1–17 (2017). https://doi.org/10.1007/s12652-017-0548-7
Abdel-Basset, M., Mohamed, M., Hussien, A.N., Sangaiah, A.K.: A novel group decision-making model based on triangular neutrosophic numbers. Soft Comput. 1–15 (2017). https://doi.org/10.1007/s00500-017-2758-5
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Broumi, S., Bakali, A., Talea, M., Smarandache, F., Uluçay, V. (2018). Minimum Spanning Tree in Trapezoidal Fuzzy Neutrosophic Environment. In: Abraham, A., Haqiq, A., Muda, A., Gandhi, N. (eds) Innovations in Bio-Inspired Computing and Applications. IBICA 2017. Advances in Intelligent Systems and Computing, vol 735. Springer, Cham. https://doi.org/10.1007/978-3-319-76354-5_3
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