Fuzzy Rough Subgroups on Approximation Space
Abstract - 206
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Keywords

Rough group
Rough subgroup
Fuzzy subgroups
Approximation space
Fuzzy rough subgroup

How to Cite

Bağırmaz, N. (2023). Fuzzy Rough Subgroups on Approximation Space . Journal of Advances in Applied & Computational Mathematics, 10, 65–70. https://doi.org/10.15377/2409-5761.2023.10.6

Abstract

Fuzzy rough sets are a mathematical concept that combines fuzzy sets and rough sets to deal with uncertainty and incompleteness in data and information. In this study, different from the definition of Dubois and Prade (1990), the fuzzy rough set is defined within the framework of the rough group concept defined by Biswas and Nanda (1994), and some of its algebraic properties are discussed. Then, the concepts of fuzzy rough subgroup and fuzzy rough normal subgroup are introduced in the rough group. In addition, some basic features and examples of these concepts are given.

MSC (2010): Primary: 03E99, 20N99.

https://doi.org/10.15377/2409-5761.2023.10.6
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References

Zadeh LA. Fuzzy sets. Inf Control1965; 8: 338-53. https://doi.org/10.1016/S0019-9958(65)90241-X

Rosenfeld A. Fuzzy groups. J Math Anal Appl. 971; 35: 512-7. https://doi.org/10.1016/0022-247X(71)90199-5

Das PS. Fuzzy groups and level subgroups. J Math Anal Appl. 1981; 84: 264-9. https://doi.org/10.1016/0022-247X(81)90164-5

Anthony JM, Sherwood H. A characterization of fuzzy subgroups. Fuzzy Sets Syst. 1982; 7: 297-305. https://doi.org/10.1016/0165-0114(82)90057-4

Pawlak Z. Rough sets. Int J Comput Inform Sci. 1982; 11: 341-56. https://doi.org/10.1007/BF01001956

Iwinski T. Algebraic approach to rough sets. Bull Polish Acad Sci Math. 1987; 35: 673-83.

Kuroki N, Wang PP. The lower and upper approximations in a fuzzy group. Inf Sci. 1996; 90: 203-20. https://doi.org/10.1016/0020-0255(95)00282-0

Cheng W, Mo Z-W, Wang J. Notes on “the lower and upper approximations in a fuzzy group” and “rough ideals in semigroups.” Inf Sci. 2007; 177: 5134-40. https://doi.org/10.1016/j.ins.2006.12.006

Li F, Zhang Z. The homomorphisms and operations of rough groups. Sci World J. 2014; 2014: 1-6. https://doi.org/10.1155/2014/507972

Wang Z, Shu L. The lower and upper approximations in a group. Int J Math Comput Sci. 2012; 6: 158-62.

Wang C, Chen D. A short note on some properties of rough groups. Comput Math Appl. 2010; 59: 431-6. https://doi.org/10.1016/j.camwa.2009.06.024

Wang C, Chen D, Hu Q. On rough approximations of groups. Int J Mach Learn Cyber. 2013; 4: 445-9. https://doi.org/10.1007/s13042-012-0108-6

Biswas R, Nanda S. Rough groups and rough subgroups. Bull Polish Acad Sci Math. 1994; 42: 251-4.

Miao D, Han S, Li D, Sun L. Rough Group, Rough Subgroup and Their Properties. In: Ślęzak D, Wang G, Szczuka M, Düntsch I, Yao Y, Eds., Rough Sets, Fuzzy Sets, Data Mining, and Granular Computing. vol. 3641. Berlin, Heidelberg: Springer; 2005. https://doi.org/10.1007/11548669

Bagirmaz N, Ozcan AF. Rough semigroups on approximation spaces. Int J Algebra. 2015; 9: 339-50. https://doi.org/10.12988/ija.2015.5742

Bağırmaz N, İçen İ, Özcan AF. Topological rough groups. Topol Algebra Appl. 2016; 4: 31-8. https://doi.org/10.1515/taa-2016-0004

Li P-Y, Liu W-L, Mou L, Guo Z-F. On separation axioms of topological rough groups. Soft Comput. 2023; 27: 57-61. https://doi.org/10.1007/s00500-022-07521-x

Pei D. A generalized model of fuzzy rough sets. Int J Gen Syst. 2005; 34: 603-13. https://doi.org/10.1080/03081070500096010

Liu G, Zhu W. The algebraic structures of generalized rough set theory. Inf Sci. 2008; 178: 4105-13. https://doi.org/10.1016/j.ins.2008.06.021

Kondo M. On the structure of generalized rough sets. Information Sciences. 2006; 176: 589-600. https://doi.org/10.1016/j.ins.2005.01.001

Dubois D, Prade H. Rough fuzzy sets and fuzzy rough sets. Int J General Syst. 1990; 17: 191-209. https://doi.org/10.1080/03081079008935107

Radzikowska AM, Kerre EE. A comparative study of fuzzy rough sets. Fuzzy Sets Syst. 2002; 126: 137-55. https://doi.org/10.1016/S0165-0114(01)00032-X

Zhan J, Liu Q. Rough fuzzy (fuzzy rough) strong H-ideals of hemirings. Ital J Pure Appl Math. 2015: 483-96.

Pan W, Zhan J. Rough fuzzy groups and rough soft groups. Rough fuzzy (fuzzy rough) strong H-ideals of hemirings. Ital J Pure Appl Math. 2016; 36: 617-28.

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Copyright (c) 2023 Nurettin Bağırmaz

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