Volume 18 , Issue 2 , PP: 199-209, 2022 | Cite this article as | XML | Html | PDF | Full Length Article
Suman Das 1 * , Rakhal Das 2 , Surapati Pramanik 3 , Binod Chandra Tripathy 4
Doi: https://doi.org/10.54216/IJNS.180204
In this article an attempt is made to introduce the notion of neutrosophic infi-topological space as an extension of infi-topological space and fuzzy infi-topological space. Besides, we define some open sets, namely, neutrosophic infi-open set, neutrosophic infi-semi-open set, neutrosophic infi-pre-open set, neutrosophic infi-b-open set. Then, we define some continuous functions namely, neutrosophic infi-continuous function, neutrosophic infi-semi-continuous function, neutrosophic infi-pre-continuous function, neutrosophic infi-b-continuous function via neutrosophic infi-topological space. Further, we formulate several interesting results on them via neutrosophic infi-topological spaces.
Neutrosophic Set, Neutrosophic Infi-Topology , Neutrosophic Infi-Open Set , Neutrosophic Infi-Continuous Function
[1] I. Arokiarani, R. Dhavaseelan, S. Jafari, & M. Parimala, On some new notations and functions in neutrosophic topological spaces. Neutrosophic Sets and Systems, 2017, v. 16, 16-19.
[2] K. Atanassov, Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 1986, v. 20, 87-96.
[3] C.L. Chang, Fuzzy topological spaces. Journal of Mathematical Analysis and Applications, 1968, v. 24, no. 1, 182-190.
[4] A. Csaszar, Generalized topology, generalized continuity. Acta Math. Hungar., 2002, v. 96, 351-357.
[5] A. Csaszar, Separation axioms for generalized topologies. Acta Math. Hungar., 2004, v. 104, 63-69.
[6] A. Csaszar, Generalized open sets in generalized topologies. Acta Math. Hungar., 2005, v. 106, no. (1-2), 53-66.
[7] A. Csaszar, Products of generalized topologies. Acta Math. Hungar., 2009, v. 123, 127-132.
[8] B. Das, B. Bhattacharya, & A.K. Saha, Some remarks on fuzzy infi topological spaces. Proyecciones Journal of Mathematics, 2021, v. 40, no. 2, 399-415.
[9] S. Das, Neutrosophic supra simply open set and neutrosophic supra simply compact space. Neutrosophic Sets and Systems, 2021, v. 43, 105-113.
[10] S. Das, R. Das, C. Granados, & A. Mukherjee, Pentapartitioned neutrosophic Q-ideals of Q-algebra. Neutrosophic Sets and Systems, 2021, v. 41, 52-63.
[11] S. Das, R. Das, & B.C. Tripathy, Multi-criteria group decision making model using single-valued neutrosophic set. LogForum, 2020, v. 16, no. 3, 421-429.
[12] S. Das, & S. Pramanik, Generalized neutrosophic b-open sets in neutrosophic topological space. Neutrosophic Sets and Systems, 2020, v. 35, 522-530.
[13] S. Das, & S. Pramanik, Neutrosophic -open sets and neutrosophic -continuous functions. Neutrosophic Sets and Systems, 2020, v. 38, 355-367.
[14] S. Das, & S. Pramanik, Neutrosophic simply soft open set in neutrosophic soft topological space. Neutrosophic Sets and Systems, 2020, v. 38, 235-243.
[15] S. Das, & S. Pramanik, Neutrosophic Tri-Topological Space. Neutrosophic Sets and Systems, 2021, v. 45, 366-377.
[16] B. Das, A.K. Saha, & B. Bhattacharya, On infi-topoogical spaces. The Journal of Fuzzy Mathematics, 2017, v. 25, no. 2, 437-448.
[17] S. Das, B. Shil, & S. Pramanik, SVPNS-MADM strategy based on GRA in SVPNS Environment. Neutrosophic Sets and Systems, 2021, v. 47, 50-65.
[18] S. Das, B. Shil, & B.C. Tripathy, Tangent similarity measure based MADM-strategy under SVPNS-environment. Neutrosophic Sets and Systems, 2021, v. 43, 93-104.
[19] R. Das, & B.C. Tripathy, Neutrosophic multiset topological space. Neutrosophic Sets and Systems, 2020, v. 35, 142-152.
[20] S. Das, & B.C. Tripathy, Pairwise neutrosophic-b-open set in neutrosophic bitopological spaces. Neutrosophic Sets and Systems, 2020, v. 38, 135-144.
[21] S. Das, & B.C. Tripathy, Neutrosophic simply b-open set in neutrosophic topological spaces. Iraqi Journal of Science, 2021, v. 62, no. 12, 4830-4838.
[22] S. Das, & B.C. Tripathy, Pentapartitioned neutrosophic topological space. Neutrosophic Sets and Systems, 2021, v. 45, 121-132.
[23] E. Ebenanjar, J. Immaculate, & C.B. Wilfred, On neutrosophic b-open sets in neutrosophic topological space. Journal of Physics Conference Series, 2018, v. 1139, no. 1, 012062.
[24] T.E. Gantner, R.C. Steinlage, & R.H. Warren, Compactness in fuzzy topological spaces. Journal of Mathematical Analysis and Applications, 1978, v. 62, no. 3, 547-562.
[25] B. Hutton, Normality in fuzzy topological spaces. Journal of Mathematical Analysis and Applications, 1975, v. 50, 74-79.
[26] P. Iswarya, & K. Bageerathi, On neutrosophic semi-open sets in neutrosophic topological spaces. International Journal of Mathematical Trends and Technology, 2016, v. 37, no. 3, 214-223.
[27] J.C. Kelly, General topology. Van Nostrand, Princeton, New Jersy, 1955.
[28] N. Levine, Semi-open sets and semi-continuity in topological spaces. Am. Math. Monthly, 1963, v. 70, 36-41.
[29] P. Majumder, S. Das, R. Das, & B.C. Tripathy, identification of the most significant risk factor of COVID-19 in economy using cosine similarity measure under SVPNS-environment. Neutrosophic Sets and Systems, 2021, v. 46, 112-127.
[30] C. Maheswari, M. Sathyabama, & S. Chandrasekar, Neutrosophic generalized b-closed sets in neutrosophic topological spaces. Journal of Physics Conference Series, 2018, v. 1139, no. 1, 012065.
[31] A.S. Masshour, A.A. Allam, F.S. Mahmud, & F.H. Khedr, On supra topological spaces. Indian J. Pure appl. Math., 1983, v. 14, no. 4, 502-510.
[32] I. Mohammed Ali Jaffer, & K. Ramesh, Neutrosophic generalized pre regular closed sets. Neutrosophic Sets and Systems, 2019, v. 30, 171-181.
[33] A. Mukherjee, & R. Das, Neutrosophic bipolar vague soft set and its application to decision making problems. Neutrosophic Sets and Systems, 2020, v. 32, 410-424.
[34] S. Pramanik, A critical review of Vivekanada’s educational thoughts for women education based on neutrosophic logic. MS Academic, 2013, v.3, no. 1, 191-198.
[35] S. Pramanik, P.P. Dey, B.C. Giri, B. C., & F. Smarandache, An extended TOPSIS for multi-attribute decision making problems with neutrosophic cubic information. Neutrosophic Sets and Systems, 2017, v.17, 20-28.
[36] S. Pramanik, S. Dalapati, S., Alam, F.., Smarandache, S., & Roy, T.K. (2018). NS-cross entropy based MAGDM under single valued neutrosophic set environment. Information, 2018, v. 9, no.2, 37.
[37] S. Pramanik, R. Mallick, & A. Dasgupta Contributions of selected Indian researchers to multi-attribute decision making in neutrosophic environment. Neutrosophic Sets and Systems, 2018, v.20, 108-131.
[38] S. Pramanik, & R. Mallick, VIKOR based MAGDM strategy with trapezoidal neutrosophic numbers. Neutrosophic Sets and Systems, 2018, v. 22, 118-130.
[39] S. Pramanik, & R. Mallick, TODIM strategy for multi-attribute group decision making in trapezoidal neutrosophic number environment. Complex & Intelligent Systems, 2019, v. 5, n.4, 379–389.
[40] S. Pramanik, Rough neutrosophic set: an overview. In F. Smarandache, & S. Broumi, Eds.), Neutrosophic theories in communication, management and information technology (pp.275-311). New York. Nova Science Publishers, 2020.
[41] S. Pramanik, & R. Mallick, MULTIMOORA strategy for solving multi-attribute group decision making (MAGDM) in trapezoidal neutrosophic number environment. CAAI Transactions on Intelligence Technology, 2020, v. 5, no. 3, 150-156.
[42] A. Pushpalatha, & T. Nandhini, Generalized closed sets via neutrosophic topological spaces. Malaya Journal of Matematik, 2019, v. 7, no. 1, 50-54.
[43] V.V. Rao, & R. Srinivasa, Neutrosophic pre-open sets and pre-closed sets in neutrosophic topology. International Journal of ChemTech Research, 2017, v. 10, no. 10, 449-458.
[44] A.K. Saha, & D. Bhattacharya, Countable fuzzy topological space and Countable fuzzy topological vector space. J. Math. Fund. Sci., 2015, v. 47, no. 2, 154-166.
[45] A.A. Salama, & S.A. Alblowi, Neutrosophic set and neutrosophic topological space. ISOR Journal of Mathematics, 2012, v. 3, no. 4, 31-35.
[46] F. Smarandache, A unifying field in logics, neutrosophy: neutrosophic probability, set and logic. Rehoboth: American Research Press, 1998.
[47] B.C. Tripathy, & S. Das, Pairwise neutrosophic b-continuous function in neutrosophic bitopological spaces. Neutrosophic Sets and Systems, 2021, v. 43, 82-92.
[48] H. Wang, F. Smarandache, Y.Q. Zhang, & R. Sunderraman, Single valued neutrosophic sets. Multispace and Multistructure, 2010, v. 4, 410-413.
L.A. Zadeh, Fuzzy sets. Information and Control, 1965, v. 8, no. 3, 338-353
