Volume 5 • Issue 1 • PP: 23–29 • 2025
Neighborhood HyperRough Set and Neighborhood SuperHyperRough Set
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© 2025 The Author(s). Published by ASPG. This article is licensed under the Creative Commons Attribution 4.0 International License (CC BY 4.0).
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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.
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References
[1] Tareq M. Al-shami and Davide Ciucci. Subset neighborhood rough sets. Knowledge-Based Systems, 237:107868, 2022.
[2] Shawkat Alkhazaleh and Emad A. Marei. New soft rough set approximations. International Journal of Fuzzy Logic and Intelligent Systems, 21:123–134, 2021.
[3] Krassimir Atanassov and George Gargov. Elements of intuitionistic fuzzy logic. part i. Fuzzy Sets and Systems, 95(1):39–52, 1998.
[4] Chunxin Bo, Xiaohong Zhang, Songtao Shao, and Florentin Smarandache. Multi-granulation neutrosophic rough sets on a single domain and dual domains with applications. Symmetry, 10:296, 2018.
[5] Said Broumi, Florentin Smarandache, and Mamoni Dhar. Rough neutrosophic sets. Infinite Study, 32:493– 502, 2014.
[6] Niladri Chatterjee, Aayush Singha Roy, and Nidhika Yadav. Soft rough set based span for unsupervised keyword extraction. Journal of Intelligent and Fuzzy Systems, 42:4379–4386, 2021.
[7] S. A. El-Sheikh, S. A. Kandil, and S. H. Shalil. Increasing and decreasing soft rough set approximations. International Journal of Fuzzy Logic and Intelligent Systems, 23:425–435, 2023.
[8] Shuyin Xia, Shulin Wu, Xinxing Chen, Guoyin Wang, Xinbo Gao, Qinghua Zhang, Elisabeth Giem, and Zizhong Chen. GRRS: Accurate and efficient neighborhood rough set for feature selection. IEEE Transactions on Knowledge and Data Engineering, 35(9):9281–9294, 2023.
[9] Shuang An, Xingyu Guo, Changzhong Wang, Ge Guo, and Jianhua Dai. A soft neighborhood rough set model and its applications. Information Sciences, 624:185– 199, 2023.
[10] Pengfei He, Xiaolong Xin, and Jianming Zhan. On rough hyperideals in hyperlattices. Journal of Applied Mathematics, 2013(1):915217, 2013.
[11] Qinghua Hu, Daren Yu, Jinfu Liu, and Congxin Wu. Neighborhood rough set based heterogeneous feature subset selection. Information Sciences, 178(18):3577– 3594, 2008.
[12] Oliver Urs Lenz, Chris Cornelis, and Daniel Peralta. Fuzzy-rough-learn 0.2: A python library for fuzzy rough set algorithms and one-class classification. In 2022 IEEE International Conference on Fuzzy Systems (FUZZ-IEEE), pages 1–8, 2022.
[13] Dmitriy Molodtsov. Soft set theory—first results. Computers & Mathematics with Applications, 37(4–5):19– 31, 1999.
[14] Zdzisław Pawlak. Rough sets. International Journal of Computer & Information Sciences, 11:341–356, 1982.
[15] Florentin Smarandache. Neutrosophy: Neutrosophic probability, set, and logic: Analytic synthesis & synthetic analysis, 1998.
[16] Florentin Smarandache. Plithogeny, Plithogenic Set, Logic, Probability, and Statistics. Pons Editions, 143 pp., Brussels, Belgium, 2017.
[17] Vicenç Torra and Yasuo Narukawa. On hesitant fuzzy sets and decision. In 2009 IEEE International Conference on Fuzzy Systems, pages 1378–1382. IEEE, 2009.
[18] Changzhong Wang, Mingwen Shao, Qiang He, Yuhua Qian, and Yali Qi. Feature subset selection based on fuzzy neighborhood rough sets. Knowledge-Based Systems, 111:173–179, 2016.
[19] Priti Madan and Alka Tripathi. Rough set model based on union neighborhood. Journal of International Academy of Physical Sciences, 27(3):207–223, 2023.
[20] Lotfi A. Zadeh. Fuzzy sets. Information and Control, 8(3):338–353, 1965.
[21] Jianming Zhan, Muhammad Irfan Ali, and Nayyar Mehmood. On a novel uncertain soft set model: Zsoft fuzzy rough set model and corresponding decision making methods. Applied Soft Computing, 56:446–457, 2017.
[22] Hu Zhao and Hongying Zhang. Some results on multigranulation neutrosophic rough sets on a single domain. Symmetry, 10:417, 2018.
[23] Kuanyun Zhu, Jingru Wang, and Yongwei Yang. A study on z-soft fuzzy rough sets in bci-algebras, 2020.
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