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Minimum Spanning Tree Problem with Single-Valued Trapezoidal Neutrosophic Numbers

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Intelligent Computing (SAI 2018)

Part of the book series: Advances in Intelligent Systems and Computing ((AISC,volume 857))

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Abstract

A single valued trapezoidal neutrosophic number (SVTNN) is a special case of single valued neutrosophic set (SVNS), which is defined on real number set. This paper investigates the single valued trapezoidal neutrosophic minimum spanning tree (SVTNMST) problem where the edge weights are assumed to be single valued trapezoidal neutrosophic variable. A neutrosophic Kruskal algorithm is presented for searching the minimum spanning tree in a single valued trapezoidal neutrosophic graph (SVTN-graph). To check the validity of the proposed algorithm, an illustrative example is explained. Finally, a comparison study has been made with Mullai’s algorithm in neutrosophic graphs.

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References

  1. Smarandache, F.: Neutrosophy. Neutrosophic Probability, Set, and Logic, Pro Quest Information & Learning, Ann Arbor, Michigan, USA, 105 p (1998)

    Google Scholar 

  2. Wang, H., Smarandache, F., Zhang, Y., Sunderraman, R.: Single valued neutrosophic sets. Multisspace Multistructure 4, 410–413 (2010)

    MATH  Google Scholar 

  3. Ye, J.: Vector similarity measures of simplified neutrosophic sets and their application in multicriteria decision making. Int. J. Fuzzy Syst. 16(2), 204–211 (2014)

    Google Scholar 

  4. Wang, H., Smarandache, F., Zhang, Y.Q., Sunderraman, R.: Interval neutrosophic sets and logic: theory and applications in computing, Hexis, Arizona (2005)

    Google Scholar 

  5. Deli, A.M., Smarandache, F.: Bipolar neutrosophic sets and their applications based on multicriteria decision making problems. In: International Conference Advanced Mechatronic Systems, (ICAMechs), pp. 249–254 (2015)

    Google Scholar 

  6. Wang, J.J., Li, X.E.: TODIM method with multi-valued neutrosophic sets. Control. Decis. 30, 1139–1142 (2015). (in Chinese)

    Google Scholar 

  7. Deli, I, Subas, Y.: A Ranking methods of single valued neutrosophic numbers and its application to multi-attribute decision making problems. Int. J. Mach. Learn. Cybern. pp. 1–14 (2016)

    Google Scholar 

  8. Thamaraiselvi, A., Santhi, R.: A new approach for optimization of real life transportation problem in neutrosophic environment. Math. Probl. Eng. 2016 (2016) article ID 5950747, 9 pages

    Article  Google Scholar 

  9. Liang, R., Wang, J.Q., Zhang, H.: A multi-criteria decision making method based on single valued trapezoidal neutrosophic preference relations with complete weight information. Neural Comput. Appl. (2017). https://doi.org/10.1007/s00521-017-2925-8

  10. Bazlamacc, F., Hindi, K.S.: Minimum-weight spanning tree algorithms: a survey and empirical study. Comput. Operat. Res. 28, 767–785 (2001)

    Article  MathSciNet  Google Scholar 

  11. Mandal, A., Dutta, J., Pal, S.C.: A new efficient technique to construct a minimum spanning tree. Int. J. Adv. Res. Comput. Sci. softw. Eng. (10), 93–97 (2012)

    Google Scholar 

  12. Dey, A., Pal, A.: Prim’s algorithm for solving minimum spanning tree problem in fuzzy environment. Ann. Fuzzy Math. Inf (2016)

    Google Scholar 

  13. Patel, N., Patel, K.M.: A survey on: enhancement of minimum spanning tree. J. Eng. Res. Appl. 5(1 (Part 3)), 06–10 (2015)

    Google Scholar 

  14. Broumi, S., Bakali, A., Talea, M., Smarandache, F., Vladareanu, L.: Computation of shortest path problem in a network with SV-trapezoidal neutrosophic numbers. In: Proceedings of the 2016 International Conference on Advanced Mechatronic Systems, Melbourne, Australia, pp. 417–422 (2016)

    Google Scholar 

  15. Broumi, S., Bakali, A., Talea, M., Smarandache, F., Vladareanu, L.: Applying dijkstra algorithm for solving neutrosophic shortest path problem. In: Proceedings of the 2016 International Conference on Advanced Mechatronic Systems, Melbourne, Australia, November 3–December 3, pp. 412–416 (2016)

    Google Scholar 

  16. 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)

    Google Scholar 

  17. Broumi, S., Bakali, A., Mohamed, T., Smarandache, F., Vladareanu, L.: Shortest path problem under triangular fuzzy neutrosophic information. In: 10th International Conference on Software, Knowledge, Information Management & Applications (SKIMA), pp. 169–174 (2016)

    Google Scholar 

  18. Broumi, S., Talea, M., Bakali, A., Smarandache, F.: Single Valued Neutrosophic Graphs. J. New Theory, N 10, 86–101 (2016)

    Google Scholar 

  19. 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)

    Google Scholar 

  20. Broumi, S., Bakali, A., Talea, M., Smarandache, F.: Isolated single valued neutrosophic graphs. Neutrosophic Sets Syst. 11, 74–78 (2016)

    Google Scholar 

  21. 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)

    Google Scholar 

  22. Broumi, S., Bakali, A., Talea, M., Smarandache, F., Verma, R.: Computing minimum spanning tree in interval valued bipolar neutrosophic environment. Int. J. Model. Optim. 7(5), 300–304 (2017). https://doi.org/10.7763/IJMO.2017.V7.602

    Article  Google Scholar 

  23. Broumi, S., Bakali, A., Talea, M., Smarandache, F., Kishore Kumar, P.K.: A new concept of matrix algorithm for MST in undirected interval valued neutrosophic graph. In: Neutrosophic Operational Research- Volume II-Florentin Smarandache, Mohamed Abdel-Basset and Victor Chang (Editors), pp. 54–69 (2017). ISBN 978-1-59973-537-

    Google Scholar 

  24. Kandasamy, I., Smarandache, F.: Clustering algorithm of triple refined indeterminate neutrosophic set for personality Grouping. In: Computing Conference 2017 (2017, in press)

    Google Scholar 

  25. Ye, J.: single valued neutrosophic minimum spanning tree and its clustering method. J. Intell. Syst. 23, 311–324 (2014)

    Google Scholar 

  26. 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)

    Article  Google Scholar 

  27. Mullai, M., Broumi, S., Stephen, A.: Shortest path problem by minimal spanning tree algorithm using bipolar neutrosophic numbers. Int. J. Math. Trends Technol. 46(2), 80–87 (2017)

    Article  Google Scholar 

  28. Kandasamy, I.: Double-valued neutrosophic sets, their minimum spanning trees, and clustering algorithm. J. Intell. Syst. 1–17 (2016)

    Google Scholar 

  29. Singh, A., Kumar, A., Appadoo, S.S.: Modified approach for optimization of real life transportation problem in neutrosophic environment. Math. Probl. Eng. (2017) 9 pages

    Google Scholar 

  30. Liang, R., Wang, J.Q., Li, L.: Multi-criteria group decision-making method based on interdependent inputs of single-valued trapezoidal neutrosophic information. Neural Comput. Appl. (2016). https://doi.org/10.1007/s00521-016-2672-2

    Article  Google Scholar 

  31. Liu, P., Zhang, X.: Some maclaurin symmetric mean operators for single-valued trapezoidal neutrosophic numbers and their applications to group decision making. Int. J. Fuzzy Syst. 1–17 (2017). https://doi.org/10.1007/s40815-017-0335-9

    Article  Google Scholar 

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Acknowledgment

The authors are very grateful to the chief editor and reviewers for their comments and suggestions, which is helpful in improving the paper.

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Authors and Affiliations

  1. Laboratory of Information Processing, Faculty of Science Ben M’Sik, University Hassan II, B.P. 7955, Sidi Othman, Casablanca, Morocco

    Said Broumi & Mohamed Talea

  2. Ecole Royale Navale, Boulevard Sour Jdid, B.P. 16303, Casablanca, Morocco

    Assia Bakali

  3. Department of Mathematic, University of New Mexico, 705 Gurley Avenue, Gallup, NM, 87301, USA

    Florentin Smarandache

  4. Department of Mathematics, Berhampur University, Bhanja Bihar -76007, Berhampur, Odisha, India

    Santanu Kumar Patro

Authors
  1. Said Broumi
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  2. Mohamed Talea
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  3. Assia Bakali
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  4. Florentin Smarandache
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  5. Santanu Kumar Patro
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Corresponding author

Correspondence to Said Broumi .

Editor information

Editors and Affiliations

  1. Faculty of Science and Engineering, Department of Information Science, Saga University, Honjo, Saga, Japan

    Kohei Arai

  2. The Science and Information (SAI) Organization, Bradford, West Yorkshire, UK

    Supriya Kapoor

  3. The Science and Information (SAI) Organization, Bradford, West Yorkshire, UK

    Rahul Bhatia

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Broumi, S., Talea, M., Bakali, A., Smarandache, F., Patro, S.K. (2019). Minimum Spanning Tree Problem with Single-Valued Trapezoidal Neutrosophic Numbers. In: Arai, K., Kapoor, S., Bhatia, R. (eds) Intelligent Computing. SAI 2018. Advances in Intelligent Systems and Computing, vol 857. Springer, Cham. https://doi.org/10.1007/978-3-030-01177-2_7

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