Neutrosophic resolving set : A novel tool for managing uncertainity in disaster resource optimization
Resumen
Neutrosophic graphs are more suitable for modelling real-life situations because real world data is often uncertain, incomplete, inconsistent, or indeterminate and neutrosophic graphs are specifically designed to handle all of neutrosophic graphs, these aspects simultaneously. In this article we introduced neutorosophic resolving set, neutorosophic resolving number, neutorosophic super resolving set, neutorosophic super resolving number, inter-valued neutorosophic resolving set, inter-valued neutorosophic resolving number, also derived some theorems, properties, corollaries and also discussed real life application based on neutrosophic resolving sets.
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Citas
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31. AL-Omeri, W.F.; Kaviyarasu, M.; Rajeshwari, M. Identifying Internet Streaming Services using Max Product of Complement in Neutrosophic Graphs. Int. J. Neutrosophic Sci. 2024, 3, 257–272. [CrossRef]
32. Yaqoob, N.; Gulistan, M.; Kadry, S.; Wahab, H.A. Complex Intuitionistic Fuzzy Graphs with Application in Cellular Network Provider Companies. Mathematics 2019, 7, 35. [CrossRef]
33. Mahapatra, R.; Samanta, S.; Pal, M.; Xin, Q. Link Prediction in Social Networks by Neutrosophic Graph. Int. J. Comput. Intell. Syst. 2020, 13, 1699–1713. [CrossRef]
34. Srisarkun, V.; Jittawiriyanukoon, C. An approximation of balanced score in neutrosophic graphs with weak edge weights. Int. J. Electr. Comput. Eng. 2021, 11, 5286–5291. [CrossRef]
35. Mahapatra, R.; Samanta, S.; Pal, M. Edge Colouring of Neutrosophic Graphs and Its Application in Detection of Phishing Website. Discret. Dyn. Nat. Soc. 2022, 2022, 1149724. [CrossRef]
36. Quek,S.G.; Selvachandran, G.; Ajay, D.; Chellamani, P.; Taniar, D.; Fujita, H.; Duong, P.; Son, L.H.; Giang, N.L. New concepts of pentapartitioned neutrosophic graphs and applications for determining safest paths and towns in response to COVID-19. Comp. Appl. Math. 2022, 41, 151. [CrossRef]
37. Alqahtani, M.; Kaviyarasu, M.; Al-Masarwah, A.; Rajeshwari, M. Application of Complex Neutrosophic Graphs in Hospital Infrastructure Design. Mathematics 2024, 12, 719. [CrossRef]
38. Wang, J.-q.; Wang, J.; Chen, Q.-h.; Zhang, H.-y.; Chen, X.-h. An outranking approach for multi-criteria decision-making with hesitant fuzzy linguistic term sets. Inf. Sci. 2014, 280, 338–351. [CrossRef]
39. Sahin, R. Multi-criteria neutrosophic decision making method based on score and accuracy functions under neutrosophic environment. Inf. Sci. 2014, 280, 338–351.
40. Broumi, S.; Sundareswaran, R.; Shanmugapriya, M.; Bakali, A.; Talea, M. Theory and Applications of Fermatean Neutrosophic Graphs. Neutrosophic Sets Syst. 2002, 50, 248–286.
2. Atanassov Krassimir, T. Intuitionistic fuzzy sets. In Intuitionistic Fuzzy Sets;
Springer: New York, NY, USA, 2019; pp. 1–137.
3. Smarandache, F. A unifying field in logics: Neutrosophic logic. In Philosophy;
American Research Press: New York, NY, USA, 1999; pp. 1–141.
4. Smarandache, F. A Unifying Field in Logics: Neutrosophic Logic. Neutrosophy,
Neutrosophic Set, Neutrosophic Probability and Statistics, 6th ed.; InfoLearnQuest:
Philadelphia, PA, USA, 2007.
5. Borzooei, R.A.; Rashmanlou, H.; Samanta, S.; Pal, M. Regularity of vague graphs. J.
Intell. Fuzzy Syst. 2016, 30, 3681–3689. [CrossRef]
6. Waseem, N.; Dudek, W.A. Certain types of edge m-polar fuzzy graphs. Iran. J.
Fuzzy Syst. 2017, 14, 27–50.
7. Ghorai, G.; Pal, M. Certain types of product bipolar fuzzy graphs. Int. J. Appl.
Comput. Math. 2017, 3, 605–619. [CrossRef]
8. Naz, S.; Rashmanlou, H.; Malik, M.A. Operations on single valued ℵGs with
application. J. Intell. Fuzzy Syst. 2017, 32, 2137–2151. [CrossRef]
9. Sahoo, S.; Pal, M. Different types of products on intuitionistic fuzzy graphs. Pac. Sci.
Rev. A Nat. Sci. Eng. 2015, 17, 87–96. [CrossRef]
10. Yang, H.-L.; Guo, Z.-L.; She, Y.; Liao, X. On single valued neutrosophic relations. J.
Intell. Fuzzy Syst. 2006, 30, 1045–1056. [CrossRef]
11. Ye, J. Single-valued neutrosophic minimum spanning tree and its clustering method.
J. Intell. Syst. 2014, 23, 311–324. [CrossRef]
12. Shannon, A.; Atanassov, K. On a generalization of intuitionistic fuzzy graphs. NIFS
2006, 12, 24–29.
13. Parvathi, R.; Karunambigai, M.G. Intuitionistic fuzzy graphs. In Computational
Intelligence, Theory and Applications; Springer: NewYork, NY, USA, 2006; pp. 139–
150.
14. Parvathi, R.; Karunambigai, M.G.; Atanassov, K.T. Operations on intuitionistic fuzzy graphs. In Proceedings of the 2009 IEEE International Conference on Fuzzy Systems, Jeju, Republic of Korea, 20–24 August 2009; pp. 1396–1401.
15. Parvathi, R.; Thamizhendhi, G. Domination in intuitionistic fuzzy graphs. Notes Intuit Fuzzy Sets 2010, 16, 39–49.
16. Rashmanlou, H.; Borzooei, R.A.; Samanta, S.; Pal, M. Properties of interval valued intuitionistic (s, t)–fuzzy graphs. Pac. Sci. Rev. ANat. Sci. Eng. 2016, 18, 30–37. [CrossRef]
17. Rashmanlou, H.; Samanta, S.; Pal, M.; Borzooei, R.A. Bipolar fuzzy graphs with categorical properties. Int. J. Comput. Intell. Syst. 2015, 8, 808–818. [CrossRef]
18. Rashmanlou, H.; Samanta, S.; Pal, M.; Borzooei, R.A. Intuitionistic fuzzy graphs with categorical properties. Fuzzy Inf. Eng. 2015, 7, 317–334. [CrossRef]
19. Smarandache, F. Extension of hypergraph to n-superhypergraph and to plithogenic n-superhypergraph, and extension of hyperalgebra to n-ary hyperalgebra. Neutrosophic Sets Syst. 2020, 33, 290–296.
20. Akram,M.Certain bipolar neutrosophic competition graphs. J. Indones. Math. Soc. 2017, 24, 1–25. [CrossRef]
21. Akram,M.; Akmal, R. Operations on intuitionistic fuzzy graph structures. Fuzzy Inf. Eng. 2016, 8, 389–410. [CrossRef]
22. Akram, M.; Dar, J.M.; Naz, S. Certain graphs under pythagorean fuzzy environment. Complex Intell. Syst. 2019, 5, 127–144. [CrossRef]
23. Akram,M.; Habib, A.; Ilyas, F.; Dar, J.M. Specific types of pythagorean fuzzy graphs and application to decision-making. Math. Comput. Appl. 2018, 23, 42. [CrossRef]
24. Akram,M.; Naz, S. Energy of pythagorean fuzzy graphs with applications. Mathematics 2018, 6, 136. [CrossRef]
25. Akram,M.; Siddique, S. Neutrosophic competition graphs with applications. J. Intell. Fuzzy Syst. 2017, 33, 921–935. [CrossRef]
26. Karaaslan, F.; Hayat, K.; Jana, C. The Determinant and Adjoint of an Interval-Valued Neutrosophic Matrix. In Neutrosophic Operational Research; Smarandache, F., Abdel-Basset, M., Eds.; Springer: Cham, Switzerland, 2021.
27. Hayat, K.; Cao, B.-Y.; Ali, M.I.; Karaaslan, F.; Qin, Z. Characterizations of Certain Types of Type 2 Soft Graphs. Discret. Dyn. Nat. Soc. 2018, 2018, 8535703. [CrossRef]
28. Karaaslan, F.; Hayat, K. Some new operations on single-valued neutrosophic matrices and their applications in multi-criteria group decision making. Appl. Intell. 2018, 48, 4594–4614. [CrossRef]
29. Majeed, A.S.; Arif, N.E. Topological indices of certain neutrosophic graphs. Aip Conf. Proc. 2023, 2845, 060024.
30. Kaviyarasu, M. On r-Edge Regular Neutrosophic Graphs. Neutrosophic Sets Syst. 2023, 53, 239–250.
31. AL-Omeri, W.F.; Kaviyarasu, M.; Rajeshwari, M. Identifying Internet Streaming Services using Max Product of Complement in Neutrosophic Graphs. Int. J. Neutrosophic Sci. 2024, 3, 257–272. [CrossRef]
32. Yaqoob, N.; Gulistan, M.; Kadry, S.; Wahab, H.A. Complex Intuitionistic Fuzzy Graphs with Application in Cellular Network Provider Companies. Mathematics 2019, 7, 35. [CrossRef]
33. Mahapatra, R.; Samanta, S.; Pal, M.; Xin, Q. Link Prediction in Social Networks by Neutrosophic Graph. Int. J. Comput. Intell. Syst. 2020, 13, 1699–1713. [CrossRef]
34. Srisarkun, V.; Jittawiriyanukoon, C. An approximation of balanced score in neutrosophic graphs with weak edge weights. Int. J. Electr. Comput. Eng. 2021, 11, 5286–5291. [CrossRef]
35. Mahapatra, R.; Samanta, S.; Pal, M. Edge Colouring of Neutrosophic Graphs and Its Application in Detection of Phishing Website. Discret. Dyn. Nat. Soc. 2022, 2022, 1149724. [CrossRef]
36. Quek,S.G.; Selvachandran, G.; Ajay, D.; Chellamani, P.; Taniar, D.; Fujita, H.; Duong, P.; Son, L.H.; Giang, N.L. New concepts of pentapartitioned neutrosophic graphs and applications for determining safest paths and towns in response to COVID-19. Comp. Appl. Math. 2022, 41, 151. [CrossRef]
37. Alqahtani, M.; Kaviyarasu, M.; Al-Masarwah, A.; Rajeshwari, M. Application of Complex Neutrosophic Graphs in Hospital Infrastructure Design. Mathematics 2024, 12, 719. [CrossRef]
38. Wang, J.-q.; Wang, J.; Chen, Q.-h.; Zhang, H.-y.; Chen, X.-h. An outranking approach for multi-criteria decision-making with hesitant fuzzy linguistic term sets. Inf. Sci. 2014, 280, 338–351. [CrossRef]
39. Sahin, R. Multi-criteria neutrosophic decision making method based on score and accuracy functions under neutrosophic environment. Inf. Sci. 2014, 280, 338–351.
40. Broumi, S.; Sundareswaran, R.; Shanmugapriya, M.; Bakali, A.; Talea, M. Theory and Applications of Fermatean Neutrosophic Graphs. Neutrosophic Sets Syst. 2002, 50, 248–286.
Publicado
2025-09-01
Número
Sección
Research Articles
Derechos de autor 2025 Boletim da Sociedade Paranaense de Matemática
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