Section
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Mathematics
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Title
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On fuzzy paratopological group and decision making during robot crash
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Author(-s)
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Muneesh Kumar A.a,
Gnanachandra P.a,
Acharjee S.b
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Affiliations
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Ayya Nadar Janaki Ammal Collegea,
Gauhati Universityb
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Abstract
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In this article, we introduce fuzzy paratopological group, fuzzy semitopological group and fuzzy quasitopological group with illustrative examples and properties. These new notions belong to fuzzy topological group. Here, we prove that each fuzzy regular paratopological group is completely regular by using fuzzy uniformities. Moreover, we prove some results related to fuzzy semitopological group and fuzzy quasitopological group. In addition, we provide an application in the area of decision making during robot crash by using our above stated notions and nano topology.
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Keywords
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fuzzy quasitopological group, fuzzy paratopological group, fuzzy quasi uniformity, robotics, decision making
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UDC
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515.1
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MSC
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54A40, 54A05, 22A05, 68T40
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DOI
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10.35634/vm230205
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Received
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27 February 2022
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Language
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English
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Citation
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Muneesh Kumar A., Gnanachandra P., Acharjee S. On fuzzy paratopological group and decision making during robot crash, Vestnik Udmurtskogo Universiteta. Matematika. Mekhanika. Komp'yuternye Nauki, 2023, vol. 33, issue 2, pp. 259-274.
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References
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- Zadeh L.A. Fuzzy sets, Information and Control, 1965, vol. 8, issue 3, pp. 338-353. https://doi.org/10.1016/S0019-9958(65)90241-X
- Chang C.L. Fuzzy topological spaces, Journal of Mathematical Analysis and Applications, 1968, vol. 24, issue 1, pp. 182-190. https://doi.org/10.1016/0022-247X(68)90057-7
- Lowen R. Fuzzy topological spaces and fuzzy compactness, Journal of Mathematical Analysis and Applications, 1976, vol. 56, issue 3, pp. 621-633. https://doi.org/10.1016/0022-247X(76)90029-9
- Rosenfeld A. Fuzzy groups, Journal of Mathematical Analysis and Applications, 1971, vol. 35, issue 3, pp. 512-517. https://doi.org/10.1016/0022-247X(71)90199-5
- Foster D.H. Fuzzy topological groups, Journal of Mathematical Analysis and Applications, 1979, vol. 67, issue 2, pp. 549-564. https://doi.org/10.1016/0022-247X(79)90043-X
- Liu Ying-Ming, Luo Mao-Kang. Fuzzy topology, Singapore: World Scientific Publishing, 1997. https://doi.org/10.1142/3281
- Liang Ma Ji, Hai Yu Chun. Fuzzy topological groups, Fuzzy Sets and Systems, 1984, vol. 12, issue 3, pp. 289-299. https://doi.org/10.1016/0165-0114(84)90075-7
- Hutton B. Uniformities on fuzzy topological spaces, Journal of Mathematical Analysis and Applications, 1977, vol. 58, issue 3, pp. 559-571. https://doi.org/10.1016/0022-247X(77)90192-5
- Lowen R. Fuzzy uniform spaces, Journal of Mathematical Analysis and Applications, 1981, vol. 82, issue 2, pp. 370-385. https://doi.org/10.1016/0022-247X(81)90202-X
- Katsaras A.K. On fuzzy uniform spaces, Journal of Mathematical Analysis and Applications, 1984, vol. 101, issue 1, pp. 97-113. https://doi.org/10.1016/0022-247X(84)90060-X
- Lellis Thivagar M., Richard C. On nano continuity, Journal of Mathematical Theory and Modeling, 2013, vol. 3, no. 7, pp. 32-37. https://iiste.org/Journals/index.php/MTM/article/view/6376/6534
- Pu Pao-Ming, Liu Ying-Ming. Fuzzy topology. I. Neighborhood structure of a fuzzy point and Moore-Smith convergence, Journal of Mathematical Analysis and Applications, 1980, vol. 76, issue 2, pp. 571-599. https://doi.org/10.1016/0022-247X(80)90048-7
- Sinha S.P. Separation axioms in fuzzy topological spaces, Fuzzy Sets and Systems, 1992, vol. 45, issue 2, pp. 261-270. https://doi.org/10.1016/0165-0114(92)90127-P
- Pu Pao-Ming, Liu Ying-Ming. Fuzzy topology. II. Product and quotient spaces, Journal of Mathematical Analysis and Applications, 1980, vol. 77, issue 1, pp. 20-37. https://doi.org/10.1016/0022-247X(80)90258-9
- Kryszkiewiec M. Rules in incomplete information systems, Information Sciences, 1999, vol. 113, issues 3-4, pp. 271-292. https://doi.org/10.1016/S0020-0255(98)10065-8
- Pawlak Z. Rough sets, International Journal of Computer and Information Sciences, 1982, vol. 11, issue 5, pp. 341-356. https://doi.org/10.1007/BF01001956
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