Pure Mathematics for Theoretical Computer Science

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Volume 5 , Issue 1 , PP: 34-47, 2025 | Cite this article as | XML | Html | PDF | Full Length Article

Neighborhood HyperRough Set and Neighborhood SuperHyperRough Set

Takaaki Fujita 1 *

  • 1 Independent Researcher, Shinjuku, Shinjuku-ku, Tokyo, Japan - (takaaki.fujita060@gmail.com)
  • Doi: https://doi.org/10.54216/PMTCS.050104

    Received: December 11, 2024 Revised: January 31, 2025 Accepted: February 28, 2025
    Abstract

    Fuzzy sets,20 rough sets,14 intuitionistic fuzzy sets,3 neutrosophic sets,15 soft sets,13 hesitant fuzzy set,17 plithogenic sets,16 and other uncertainty-handling frameworks have been the focus of intensive and ongoing research. Rough set theory provides a mathematical framework for approximating subsets through lower and upper approximations defined by equivalence relations, effectively capturing uncertainty in classification and data analysis.5, 10 Building upon these foundational concepts, further generalizations such as Hyperrough Sets8 and Superhyperrough Sets have been introduced. In this paper, we investigate the concepts of Neighborhood Hyperrough Sets and Neighborhood Superhyperrough Sets. These models extend the classical Neighborhood Rough Set framework by incorporating the structural richness of Hyperrough Sets and Superhyperrough Sets.

    Keywords :

    Rough set , Hyperrough Set , Neighborhood Rough Set , SuperHyperRough set

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    Cite This Article As :
    Fujita, Takaaki. Neighborhood HyperRough Set and Neighborhood SuperHyperRough Set. Pure Mathematics for Theoretical Computer Science, vol. , no. , 2025, pp. 34-47. DOI: https://doi.org/10.54216/PMTCS.050104
    Fujita, T. (2025). Neighborhood HyperRough Set and Neighborhood SuperHyperRough Set. Pure Mathematics for Theoretical Computer Science, (), 34-47. DOI: https://doi.org/10.54216/PMTCS.050104
    Fujita, Takaaki. Neighborhood HyperRough Set and Neighborhood SuperHyperRough Set. Pure Mathematics for Theoretical Computer Science , no. (2025): 34-47. DOI: https://doi.org/10.54216/PMTCS.050104
    Fujita, T. (2025) . Neighborhood HyperRough Set and Neighborhood SuperHyperRough Set. Pure Mathematics for Theoretical Computer Science , () , 34-47 . DOI: https://doi.org/10.54216/PMTCS.050104
    Fujita T. [2025]. Neighborhood HyperRough Set and Neighborhood SuperHyperRough Set. Pure Mathematics for Theoretical Computer Science. (): 34-47. DOI: https://doi.org/10.54216/PMTCS.050104
    Fujita, T. "Neighborhood HyperRough Set and Neighborhood SuperHyperRough Set," Pure Mathematics for Theoretical Computer Science, vol. , no. , pp. 34-47, 2025. DOI: https://doi.org/10.54216/PMTCS.050104