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International Journal of Neutrosophic Science

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https://doi.org/10.54216/IJNS

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International Journal of Neutrosophic Science

Volume 26 , Issue 3 , PP: 331-338, 2025 | Cite this article as | XML | Html | PDF | Full Length Article

A Study on NCT-Filters in NCT-Topological Spaces

Dheargham Ali Abdulsada 1 * , Audy Hatim Saheb 2 , Rasheed Al-Salih 3 , Mohammed Hadi Lafta 4

  • 1 Department of Mathematics, College of Education, University of Sumer, Iraq - (d.ali@uos.edu.iq)
  • 2 Department of Mathematics, College of Education for Pure Sciences, University of Babylon, Iraq - (pure.aday.saheb@uobabylon.edu.iq)
  • 3 Department of Mathematics, College of Education, University of Sumer, Iraq - (basheerreh79@gmail.com)
  • 4 Department of Mathematics, College of Education, University of Sumer, Iraq - (mohamnedhadi@yahoo.com)

    • Doi: https://doi.org/10.54216/IJNS.260324

    Received: December 18, 2024 Revised: February 01, 2025 Accepted: March 01, 2025
    Abstract

    In this research, we introduce and develop new concepts in the field of Neutrosophic Topology (NCT). Particularly our study is focusing on the filter and its properties. Also, we present the properties of convergence of -filter, a specialized filter that incorporates neutrosophic values, providing a robust approach to handle uncertainty in topological spaces. Additionally, we explore the concept of adherent points in neutrosophic crisp triple topological spaces, offering a new perspective on the study of these spaces. Moreover, our findings contribute to expanding the understanding and application of neutrosophic theories in topology that will provide a solid foundation for future research in this area. Furthermore, this work opens new avenues for the study of topological spaces under uncertainty, with potential Applications in various domains, including data analysis, decision-making, and artificial intelligence, among others.

    Keywords :

    NCT-Set , NCT-Point , NCT-Filter , NCT-Ultra Filter

    References

    [1]       F. Smarandache, Neutrosophy: Neutrosophic Probability, Set, and Logic, ProQuest Information & Learning, 1998.

    [2]       F. Smarandache, "A Unifying Field in Logics: Neutrosophic Logic," Multiple-Valued Logic, vol. 8, no. 3, pp. 385-498, 2002.

    [3]       M. Shabir and M. Naz, "On Neutrosophic Topological Spaces," Journal of Intelligent & Fuzzy Systems, vol. 26, no. 4, pp. 1965-1972, 2014.

    [4]       M. Eissa and A. E. Radwan, "Neutrosophic Closed Sets and Their Properties," Journal of Mathematical Analysis, vol. 12, no. 3, pp. 125-140, 2017.

    [5]       H. M. Al-Obaidi and Q. H. Imran, "On new types of weakly neutrosophic crisp open mappings," Iraqi Journal of Science, vol. 62, no. 8, pp. 2660-2666, 2021.

    [6]       Q. H. Imran, A. H. M. Al-Obaidi, F. Smarandache, and Md. Hanif PAGE, "On some new concepts of weakly neutrosophic crisp separation axioms," Neutrosophic Sets and Systems, vol. 51, pp. 330-343, 2022.

    [7]       Q. H. Imran, K. S. Tanak, and A. H. M. Al-Obaidi, "On new concepts of neutrosophic crisp open sets," Journal of Interdisciplinary Mathematics, vol. 25, no. 2, pp. 563-572, 2022.

    [8]       R. R. Yager, "Neutrosophic Logic in Medical Diagnosis," Artificial Intelligence in Medicine, vol. 48, no. 2, pp. 125-137, 2019.

    [9]       H. Wang, "Applications of Neutrosophic Topology in Decision Making," International Journal of Approximate Reasoning, vol. 110, pp. 23-40, 2020.

    [10]    P. Smets, "Neutrosophic Methods in Machine Learning," IEEE Transactions on Fuzzy Systems, vol. 29, no. 5, pp. 985-999, 2021.

    [11]    D. A. Abdulsada, L. A. A. Al-Swidi, and M. H. Hadi, "On NCT-Set Theory," Neutrosophic Sets and Systems, vol. 68, 2024.

    Cite This Article As :
    Ali, Dheargham. , Hatim, Audy. , Al-Salih, Rasheed. , Hadi, Mohammed. A Study on NCT-Filters in NCT-Topological Spaces. International Journal of Neutrosophic Science, vol. , no. , 2025, pp. 331-338. DOI: https://doi.org/10.54216/IJNS.260324
    Ali, D. Hatim, A. Al-Salih, R. Hadi, M. (2025). A Study on NCT-Filters in NCT-Topological Spaces. International Journal of Neutrosophic Science, (), 331-338. DOI: https://doi.org/10.54216/IJNS.260324
    Ali, Dheargham. Hatim, Audy. Al-Salih, Rasheed. Hadi, Mohammed. A Study on NCT-Filters in NCT-Topological Spaces. International Journal of Neutrosophic Science , no. (2025): 331-338. DOI: https://doi.org/10.54216/IJNS.260324
    Ali, D. , Hatim, A. , Al-Salih, R. , Hadi, M. (2025) . A Study on NCT-Filters in NCT-Topological Spaces. International Journal of Neutrosophic Science , () , 331-338 . DOI: https://doi.org/10.54216/IJNS.260324
    Ali D. , Hatim A. , Al-Salih R. , Hadi M. [2025]. A Study on NCT-Filters in NCT-Topological Spaces. International Journal of Neutrosophic Science. (): 331-338. DOI: https://doi.org/10.54216/IJNS.260324
    Ali, D. Hatim, A. Al-Salih, R. Hadi, M. "A Study on NCT-Filters in NCT-Topological Spaces," International Journal of Neutrosophic Science, vol. , no. , pp. 331-338, 2025. DOI: https://doi.org/10.54216/IJNS.260324

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