Volume 25 , Issue 3 , PP: 349-362, 2025 | Cite this article as | XML | Html | PDF | Full Length Article
S. Sathyapriya 1 * , V. Jeyanthi 2 , Said Broumi 3
Doi: https://doi.org/10.54216/IJNS.250331
In this article, we introduce and establish a novel concept called ’cubic spherical linguistic neutrosophic topological spaces’ by employing cubic spherical linguistic neutrosophic sets and topological frameworks. Various foundational definitions, theorems, and properties are provided along with illustrative examples.
Cubic Spherical Linguistic Neutrosophic topological Space , Cubic Spherical Linguistic Neutrosophic open set , Cubic Spherical Linguistic Neutrosophic closed set , Cubic Spherical Linguistic Neutrosophic continuous function , Cubic Spherical Linguistic Neutrosophic derived sets
[1] Atanassov, K.T. Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 1986, 20, pp. 87–96.
[2] Chang, C.L. Fuzzy topological spaces. J. Math. Anal. Appl., 1968, 24, pp. 182–190.
[3] Chen, Z.C.; Liu, P.H.; Pei, Z. An approach to multiple attribute group decision making based on linguistic intuitionistic fuzzy numbers. Int. J. Comput. Intell. Syst., 2015, 8, 747–760.
[4] Coker, D. An introduction to intuitionistic fuzzy topological spaces. Fuzzy Sets and Systems, 1997, 88, pp. 81-89.
[5] Fan, Feng, and Hu. Linguistic Neutrosophic Numbers Einstein Operator and Its Application in Decision Making. Mathematics, 2019, 7(5), 389. doi:10.3390/math7050389.
[6] Fang, Zebo and Te, Jun. Multiple Attribute Group Decision-Making Method Based on Linguistic Neutrosophic Numbers. Symmetry, 2017, 9(7), 111; https://doi.org/10.3390/sym9070111.
[7] Gayathri, N., & Helen, M. (2021). Linguistic Neutrosophic Topology. Neutrosophic Sets and Systems, 46, 254–267.
[8] Garg H and Nancy. Linguistic single-valued neutrosophic power aggregation operators and their applications to group decision-making problems. IEEE/CAA J. Autom. Sinica, 2020, vol. 7, no. 2, pp. 546–558.
[9] S. Gomathi, S. Krishnaprakash, M. Karpagadevi, Said Broumi. ”Cubic Spherical Neutrosophic Sets.”International Journal of Neutrosophic Science, 21(4) 2023, 172-180. https://doi.org/10.54216/IJNS.210418.
[10] S. Gomathi, S. Krishnaprakash, M. Karpagadevi, S. Krishnaprakash, ”Cubic Spherical Neutrosophic Topological Spaces.”South East Asian Journal of Mathematics and Mathematical Sciences, 20(1) 2024, 223-232. https://doi.10.56827/SEAJMMS.2024.2001.17.
[11] Herrera, F.; Herrera-Viedma, E.; Verdegay, L. A model of consensus in group decision making under linguistic assessments. Fuzzy Sets Syst., 1996, 79, 73–87.
[12] Herrera, F.; Herrera-Viedma, E. Linguistic decision analysis: Steps for solving decision problems under linguistic information. Fuzzy Sets and Systems, 2000, 115(1), 67–82.
[13] Munkres, James R. Topology: a First Course. Englewood Cliffs, N.J.: Prentice-Hall, 1974.
[14] Smarandache, F. A unifying field in logics. Neutrosophy: Neutrosophic probability, set and logic. American Research Press, Rehoboth, 1999.
[15] Su, Z.S. Deviation measures of linguistic preference relations in group decision making. Omega, 2005, 33(3), 249–254.
[16] Wang, H.; Smarandache, F.; Zhang, T.Q.; Sunderraman, R. Interval neutrosophic sets and logic: Theory and applications in computing. Hexis, Phoenix, AZ, 2005.
[17] Wei, G.; Wu, J.; Guo, Y.; Wang, J.; Wei, C. An extended COPRAS model for multiple attribute group decision making based on single-valued neutrosophic 2-tuple linguistic environment. Technological and Economic Development of Economy, 2021, 27(2), 353-368. https://doi.org/10.3846/tede.2021.14057.
[18] Ye, J. (2015). An extended TOPSIS method for multiple attribute group decision making based on single valued neutrosophic linguistic numbers. Journal of Intelligent & Fuzzy Systems, 28, 247–255.
[19] Zadeh, L.A. (1965). Fuzzy Sets. Information and Control, 8, 338–353.
[20] Zadeh, L.A. (1975). The concept of a linguistic variable and its application to approximate reasoning Part I. Information Sciences, 8, 199–249.