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Single-Valued Neutrosophic Rough Continuous Mapping via Single-Valued Neutrosophic Rough Topological Space

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Transactions on Rough Sets XXIII

Abstract

In this article an attempt is made to introduce and study the notion of single-valued neutrosophic rough continuous mapping, single-valued neutrosophic rough compactness via single-valued neutrosophic rough topological spaces (SVNRTS). By defining the concept of single-valued neutrosophic rough continuous function, single-valued neutrosophic rough compactness, we formulate and discuss several interesting results on SVNRTSs.

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References

  1. Arokiarani, I., Dhavaseelan, R., Jafari, S., Parimala, M.: On some new notations and functions in neutrosophic topological spaces. Neutrosophic Sets Syst. 16, 16–19 (2017)

    Google Scholar 

  2. Atanassov, K.: Intuitionistic fuzzy sets. Fuzzy Sets Syst. 20, 87–96 (1986)

    Article  MATH  Google Scholar 

  3. Broumi, S., Smarandache, F., Dhar, M.: Rough neutrosophic sets. Neutrosophic Sets Syst. 3, 60–65 (2014)

    MATH  Google Scholar 

  4. Das, S., Das, R., Granados, C.: Topology on quadripartitioned neutrosophic sets. Neutrosophic Sets Syst. 45, 54–61 (2021). https://doi.org/10.5281/zenodo.5485442

    Article  Google Scholar 

  5. Das, S., Das, R., Tripathy, B.C.: Topology on rough pentapartitioned neutrosophic set. Iraqi J. Sci. (in Press)

    Google Scholar 

  6. Das, S., Pramanik, S.: Generalized neutrosophic \(b\)-open sets in neutrosophic topological space. Neutrosophic Sets Syst. 35, 522–530 (2020)

    Google Scholar 

  7. Das, S., Pramanik, S.: Neutrosophic \(\Phi \)-open sets and neutrosophic \(\Phi \)-continuous functions. Neutrosophic Sets Syst. 38, 355–367 (2020)

    Google Scholar 

  8. Das, S., Tripathy, B.C.: Neutrosophic simply b-open set in neutrosophic topological spaces. Iraqi J. Sci. (in Press)

    Google Scholar 

  9. Ebenanjar, E., Immaculate, J., Wilfred, C.B.: On neutrosophic b-open sets in neutrosophic topological space. J. Phys. Conf. Ser. 1139(1), 012062 (2018)

    Article  Google Scholar 

  10. Iswarya, P., Bageerathi, K.: On neutrosophic semi-open sets in neutrosophic topological spaces. Int. J. Math. Trends Technol. 37(3), 214–223 (2018)

    Article  Google Scholar 

  11. Jayaparthasarathy, G., Arockia Dasan, M., Little Flower, V.F., Ribin Christal, R.: New open sets in N-neutrosophic supra topological spaces. Neutrosophic Sets Syst. 31, 44–62 (2020)

    Google Scholar 

  12. Jayaparthasarathy, G., Little Flower, V.F., Arockia Dasan, M.: Neutrosophic supra topological applications in data mining process. Neutrosophic Sets Syst. 27, 80–97 (2019)

    Google Scholar 

  13. Jin, Q., Hu, K., Bo, C., Li, L.: A new single-valued neutrosophic rough sets and related topology. J. Math. 1–14 (2021). Article ID 5522021. https://doi.org/10.1155/2021/5522021

  14. Lellis Thivagar, M., Jafari, S., Sutha Devi, V., Antonysamy, V.: A novel approach to nano topology via neutrosophic sets. Neutrosophic Sets Syst. 20, 86–94 (2018)

    Google Scholar 

  15. Maheswari, C., Sathyabama, M., Chandrasekar, S.: Neutrosophic generalized \(b\)-closed sets in neutrosophic topological spaces. J. Phys. Conf. Ser. 1139(1), 012065 (2018)

    Article  Google Scholar 

  16. Mohammed Ali Jaffer, I., Ramesh, K.: Neutrosophic generalized pre regular closed sets. Neutrosophic Sets Syst. 30, 171–181 (2019)

    Google Scholar 

  17. Mondal, K., Pramanik, S.: Decision making based on some similarity measures under interval rough neutrosophic environment. Neutrosophic Sets Syst. 10, 46–57 (2015)

    Google Scholar 

  18. Mondal, K., Pramanik, S.: Rough neutrosophic multi-attribute decision-making based on rough accuracy score function. Neutrosophic Sets Syst. 8, 16–22 (2015)

    Google Scholar 

  19. Mondal, K., Pramanik, S.: Rough neutrosophic multi-attribute decision-making based on grey relational analysis. Neutrosophic Sets Syst. 7, 8–17 (2015)

    Google Scholar 

  20. Mondal, K., Pramanik, S., Giri, B.C.: Rough neutrosophic aggregation operators for multi-criteria decision-making. In: Kahraman, C., Otay, İ (eds.) Fuzzy Multi-criteria Decision-Making Using Neutrosophic Sets. SFSC, vol. 369, pp. 79–105. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-00045-5_5

    Chapter  Google Scholar 

  21. Mondal, K., Pramanik, S., Smarandache, F.: Rough neutrosophic TOPSIS for multi-attribute group decision making. Neutrosophic Sets Syst. 13, 105–117 (2016)

    Google Scholar 

  22. Mondal, K., Pramanik, S., Smarandache, F.: Multi-attribute decision making based on rough neutrosophic variational coefficient similarity measure. Neutrosophic Sets Syst. 13, 3–17 (2016)

    Google Scholar 

  23. Mondal, K., Pramanik, S., Smarandache, F.: Rough neutrosophic hyper-complex set and its application to multi attribute decision making. Crit. Rev. XIII, 111–123 (2016)

    Google Scholar 

  24. Nanda, S., Majumdar, S.: Fuzzy rough sets. Fuzzy Sets Syst. 45, 157–160 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  25. Pawlak, Z.: Rough sets. Int. J. Inf. Comput. Sci. 11(5), 341–356 (1982)

    Article  MATH  Google Scholar 

  26. Pawlak, Z., Sowinski, R.: Rough set approach to multi attribute decision analysis. Eur. J. Oper. Res. 72(3), 443–459 (1994)

    Article  MATH  Google Scholar 

  27. Pramanik, S.: Interval quadripartitioned neutrosophic sets. Neutrosophic Sets Syst. (in Press)

    Google Scholar 

  28. Pramanik, S., Mondal, K.: Some rough neutrosophic similarity measures and their application to multi attribute decision making. Glob. J. Eng. Sci. Res. Manag. 2(7), 61–74 (2015)

    Google Scholar 

  29. Pramanik, S., Mondal, K.: Rough bipolar neutrosophic set. Glob. J. Eng. Sci. Res. Manag. 3(6), 71–81 (2016)

    Google Scholar 

  30. Pramanik, S., Mondal, K.: Cosine similarity measure of rough neutrosophic sets and its application in medical diagnosis. Glob. J. Adv. Res. 2(1), 212–220 (2015)

    Google Scholar 

  31. Pramanik, S., Roy, R., Roy, T.K., Smarandache, F.: Multi criteria decision making using correlation coefficient under rough neutrosophic environment. Neutrosophic Sets Syst. 17, 29–36 (2017)

    Google Scholar 

  32. Pramanik, S., Roy, R., Roy, T.K.: Multi criteria decision making based on projection and bidirectional projection measures of rough neutrosophic sets. Neutrosophic Sets Syst. 19, 101–109 (2018)

    Google Scholar 

  33. Pushpalatha, A., Nandhini, T.: Generalized closed sets via neutrosophic topological spaces. Malaya J. Matematik 7(1), 50–54 (2019)

    Article  Google Scholar 

  34. Rao, V.V., Srinivasa, R.: Neutrosophic pre-open sets and pre-closed sets in neutrosophic topology. Int. J. ChemTech Res. 10(10), 449–458 (2017)

    Google Scholar 

  35. Riaz, M., Smarandache, F., Karaaslan, F., Hashmi, M.R., Nawaz, I.: Neutrosophic soft rough topology and its applications to multi-criteria decision-making. Neutrosophic Sets Syst. 35, 198–219 (2020)

    Google Scholar 

  36. Roy, R., Pramanik, S., Roy, T.K.: Interval rough neutrosophic TOPSIS strategy for multi-attribute decision making. In: Neutrosophic Sets in Decision Analysis and Operations Research, 21 p (2020). https://doi.org/10.4018/978-1-7998-2555-5.ch005

  37. Smarandache, F.: A Unifying Field in Logics, Neutrosophy: Neutrosophic Probability, Set and Logic. Rehoboth, American Research Press (1998)

    Google Scholar 

  38. Salama, A.A., Alblowi, S.A.: Neutrosophic set and neutrosophic topological space. ISOR J. Math. 3(4), 31–35 (2012)

    Article  Google Scholar 

  39. Sweety, C.A.C., Arockiarani, I.: Topological structures of fuzzy neutrosophic rough sets. Neutrosophic Sets Syst. 9, 50–57 (2015)

    Google Scholar 

  40. Vijayalakshmi, R., Mookambika, A.P.: Properties of neutrosophic nano semi open sets. Malaya J. Matematik 8(4), 1851–1858 (2020)

    Article  Google Scholar 

  41. Wang, H., Madiraju, P., Zhang, Y.Q., Sunderraman, R.: Interval neutrosophic sets. Int. J. Appl. Math. Stat. 3(5), 1–18 (2005)

    MathSciNet  Google Scholar 

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

    MATH  Google Scholar 

  43. Zadeh, L.A.: Fuzzy sets. Inf. Control 8, 338–353 (1965)

    Article  MATH  Google Scholar 

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Acknowledgement

The author thanks the reviewer for the careful reading of the paper and the constrictive comments. The comments helped in improving the clarity of presentation of the paper.

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Correspondence to Binod Chandra Tripathy .

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Tripathy, B.C., Das, S., Das, R. (2022). Single-Valued Neutrosophic Rough Continuous Mapping via Single-Valued Neutrosophic Rough Topological Space. In: Peters, J.F., Skowron, A., Bhaumik, R.N., Ramanna, S. (eds) Transactions on Rough Sets XXIII. Lecture Notes in Computer Science(), vol 13610. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-66544-2_6

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  • DOI: https://doi.org/10.1007/978-3-662-66544-2_6

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