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Neutrosophic pre-I-open set in neutrosophic ideal bitopological space

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Abstract

In this article, we introduce the notion of neutrosophic ideal bitopological space (NIBTS) by generalizing the idea of neutrosophic ideal topological space (NITS). Besides, we procure the notion of local function on neutrosophic bitopological space (NBTS) and studied its different properties. Further, we procure the concept of neutrosophic pre-I-open set (NPIOS), neutrosophic semi-I-open set (NSIOS), neutrosophic b-I-open set (N-b-IOS), neutrosophic α-I-open set (N-α-IOS) via NIBTSs. By defining NPIOS, NSIOS, N-b-IOS, N-α-IOS, we establish several interesting results on NIBTS in the form of theorem, proposition, lemma, etc.

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References

  • Albowi SA, Salama AA, Eisa M (2013) New concepts of neutrosophic sets. Int J Math Comput Appl Res 3(4):95–102

    Google Scholar 

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

    Google Scholar 

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

    Article  MATH  Google Scholar 

  • Chang CL (1968) Fuzzy topological spaces. J Math Anal Appl 24

  • Coker D (1997) An introduction to intuitionistic fuzzy topological spaces. Fuzzy Sets Syst 88:81–89

    Article  MathSciNet  MATH  Google Scholar 

  • Das S (2021) Neutrosophic supra simply open set and neutrosophic supra simply compact space. Neutrosophic Sets Syst 43:105–113

    Google Scholar 

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

    Google Scholar 

  • Das S, Pramanik S (2020b) Neutrosophic Φ-open sets and neutrosophic Φ-continuous functions. Neutrosophic Sets Syst 38:355–367

    Google Scholar 

  • Das R, Tripathy BC (2020a) Neutrosophic Multiset Topological Space. Neutrosophic Sets Syst 35:142–152

    Google Scholar 

  • Das S, Tripathy BC (2020b) Pairwise neutrosophic-b-open set in neutrosophic bitopological spaces. Neutrosophic Sets Syst 38:135–144

    Google Scholar 

  • Dhavaseelan R, Jafari S (2018) Generalized neutrosophic closed sets. In: F. Smarandache, S. Pramanik (Eds., vol.2), New trends in neutrosophic theory and applications, pp. 261–273. Brussels,Pons Editionshttps://doi.org/10.3390/math6050067.

  • Ebenanjar E, Immaculate J, Wilfred CB (2018) On neutrosophic b -open sets in neutrosophic topological space. J Phys Conf Ser 1139(1):012–062

    Google Scholar 

  • Ganesan S, Smarandache F (2021) Neutrosophic biminimal α-open sets. Bull Int Math Virtual Inst 11(3):545–553

    Google Scholar 

  • Gani AN, Bhanu JR (2021) Fuzzy pairwise gamma semicontinuity and fuzzy pairwise gamma semicompactness in fuzzy bitopological spaces. Adv Appl Math Sci 20(5):945–965

    Google Scholar 

  • Ibedou I (2014) Separation axioms in fuzzy bitopological spaces. J Intell Fuzzy Syst 27:943–951

    Article  MathSciNet  MATH  Google Scholar 

  • Imran QH, Dhavaseelan R, Al-Obaidi AHM, Page MH (2020) On neutrosophic generalized alpha generalized continuity. Neutrosophic Sets Syst 35:511–521

    Google Scholar 

  • Imran QH, Smarandache F, Al-Hamido RK, Dhavaseelan R (2017) On neutrosophic semi-α-open sets. Neutrosophic Sets Syst 18:37–42

    Google Scholar 

  • Iswarya P, Bageerathi K (2016) On neutrosophic semi-open sets in neutrosophic topological spaces. Int J Math Trends Technol 37(3):214–223

    Article  Google Scholar 

  • Jeya Puvaneswari P, Bageerathi K (2017) On Neutrosophic feebly open set in neutrosophic topological spaces. Int J Math Trends Technol 41(3):230–237

    Article  Google Scholar 

  • Kandil A, El-Shafee ME (1989) Biproximities and fuzzy bitopological spaces. Simon Stevin 63(1):45–66

    MathSciNet  MATH  Google Scholar 

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

    Article  Google Scholar 

  • Mukherjee A, Das R (2020) Neutrosophic Bipolar vague soft set and its application to decision making problems. Neutrosophic Sets Syst 32:410–424

    Google Scholar 

  • Mwchahary DD, Basumatary B (2020) A Note on Neutrosophic Bitopological Spaces. Neutrosophic Sets Syst 33:134–144

    Google Scholar 

  • Ozturk TY, Ozkan A (2019) Neutrosophic bitopological spaces. Neutrosophic Sets Syst 30:88–97

    Google Scholar 

  • Page MH, Imran QH (2020) Neutrosophic generalized homeomorphism. Neutrosophic Sets Syst 35:340–346

    Google Scholar 

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

    Article  Google Scholar 

  • Rao VV, Srinivasa R (2017) Neutrosophic pre-open sets and pre-closed sets in neutrosophic topology. Int J Chem Tech Res 10(10):449–458

    Google Scholar 

  • Salama AA, Alblowi SA (2012a) Neutrosophic set and neutrosophic topological space. ISOR J Math 3(4):31–35

    Article  Google Scholar 

  • Salama AA, Alblowi SA (2012b) Generalized neutrosophic set and generalized neutrosophic topological space. Comput Sci Eng 2(7):129–132

    Article  Google Scholar 

  • Salama AA, Smarandache F (2014) Neutrosophic ideal theory: neutrosophic local function and generated neutrosophic topology. neutrosophic theory and its applications. Collect Papers I:213–218

    Google Scholar 

  • Salama AA, Smarandache F, Alblowi SA (2014a) New neutrosophic crisp topological concepts. Neutrosophic Sets Syst 4:50–54

    Google Scholar 

  • Salama AA, Smarandache F, Valeri K (2014b) Neutrosophic closed set and Neutrosophic continuous functions. Neutrosophic Sets Syst 4:4–8

    Google Scholar 

  • Sarkar D (1997) Fuzzy ideal theory. Fuzzy Local Func Generat Fuzzy Topol Fuzzy Sets Syst 87(1):117–123

    MATH  Google Scholar 

  • Shanthi VK, Chandrasekar S, Safina Begam K (2018) Neutrosophic generalized semi closed sets in neutrosophic topological spaces. Int J Res Advent Technol 67:1739–1743

    Google Scholar 

  • Smarandache F (2002) Neutrosophy and Neutrosophic Logic, First International Conference on Neutrosophy, Neutrosophic Logic, Set, Probability, and Statistics. University of New Mexico, Gallup, NM 87301, USA

  • Smarandache F (1998) A unifying field in logics, neutrosophy: neutrosophic probability, set and logic. American Research Press, Rehoboth

    MATH  Google Scholar 

  • Sreeja D, Sarankumar T (2018) Generalized Alpha Closed sets in Neutrosophic topological spaces. J Appl Sci Comput 5(11):1816–1823

    Google Scholar 

  • Suresh R, Palaniammal S (2020) Neutrosophic weakly generalized open and closed sets. Neutrosophic Sets Syst 33:67–77

    Google Scholar 

  • Tripathy BC, Das S (2021) Pairwise Neutrosophic b-continuous function in neutrosophic bitopological spaces. Neutrosophic Sets Syst 43:82–92

    Google Scholar 

  • Tripathy BC, Ray GC (2013) Mixed fuzzy ideal topological spaces. Appl Math Comput 220:602–607

    Article  MathSciNet  MATH  Google Scholar 

  • Tripathy BC, Ray GC (2018) Fuzzy δ-I-continuity in mixed fuzzy ideal topological spaces. J Appl Anal 24(2):233–239

    Article  MathSciNet  MATH  Google Scholar 

  • Zadeh LA (1965) Fuzzy sets. Inf Control 8(3):338–353

    Article  MATH  Google Scholar 

Download references

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  1. Department of Mathematics, Tripura University, Agartala, Tripura, 799022, India

    Suman Das, Rakhal Das & Binod Chandra Tripathy

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  1. Suman Das
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  2. Rakhal Das
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  3. Binod Chandra Tripathy
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Correspondence to Rakhal Das.

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Das, S., Das, R. & Tripathy, B.C. Neutrosophic pre-I-open set in neutrosophic ideal bitopological space. Soft Comput 26, 5457–5464 (2022). https://doi.org/10.1007/s00500-022-06994-0

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