On the characterization of Pythagorean fuzzy subgroups

Supriya Bhunia; Ganesh Ghorai; Qin Xin; Supriya Bhunia; Ganesh Ghorai; Qin Xin

doi:10.3934/math.2021058

AIMS Mathematics

2021, Volume 6, Issue 1: 962-978. doi: 10.3934/math.2021058

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Research article

On the characterization of Pythagorean fuzzy subgroups

1.
Department of Applied Mathematics with Oceanology and Computer Programming, Vidyasagar University, Midnapore 721102, India
2.
Faculty of Science and Technology, University of the Faroe Islands, Vestarabryggja 15, FO 100 Torshavn, Faroe Islands

Received: 13 August 2020 Accepted: 22 October 2020 Published: 05 November 2020
MSC : 03E72, 08A72, 20N25

Pythagorean fuzzy environment is the modern tool for handling uncertainty in many decisions making problems. In this paper, we represent the notion of Pythagorean fuzzy subgroup (PFSG) as a generalization of intuitionistic fuzzy subgroup. We investigate various properties of our proposed fuzzy subgroup. Also, we introduce Pythagorean fuzzy coset and Pythagorean fuzzy normal subgroup (PFNSG) with their properties. Further, we define the notion of Pythagorean fuzzy level subgroup and establish related properties of it. Finally, we discuss the effect of group homomorphism on Pythagorean fuzzy subgroup.
- Pythagorean fuzzy set,
- Pythagorean fuzzy subgroup,
- Pythagorean fuzzy coset,
- Pythagorean fuzzy normal subgroup,
- Pythagorean fuzzy level subgroup
Citation: Supriya Bhunia, Ganesh Ghorai, Qin Xin. On the characterization of Pythagorean fuzzy subgroups[J]. AIMS Mathematics, 2021, 6(1): 962-978. doi: 10.3934/math.2021058

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Abstract

Pythagorean fuzzy environment is the modern tool for handling uncertainty in many decisions making problems. In this paper, we represent the notion of Pythagorean fuzzy subgroup (PFSG) as a generalization of intuitionistic fuzzy subgroup. We investigate various properties of our proposed fuzzy subgroup. Also, we introduce Pythagorean fuzzy coset and Pythagorean fuzzy normal subgroup (PFNSG) with their properties. Further, we define the notion of Pythagorean fuzzy level subgroup and establish related properties of it. Finally, we discuss the effect of group homomorphism on Pythagorean fuzzy subgroup.

References

[1]	L. A. Zadeh, Fuzzy sets, Inform. Contr., 8 (1965), 338-353.
[2]	A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512-517.
[3]	J. M. Anthony, H. Sherwood, Fuzzy groups redefined, J. Math. Anal. Appl., 69 (1979), 124-130.
[4]	J. M. Anthony, H. Sherwood, A characterization of fuzzy subgroups, Fuzzy Set. Syst., 7 (1982), 297-305. doi: 10.1016/0165-0114(82)90057-4
[5]	P. S. Das, Fuzzy groups and level subgroups, J. Math. Anal. Appl., 84 (1981), 264-269. doi: 10.1016/0022-247X(81)90164-5
[6]	F. P. Choudhury, A. B. Chakraborty, S. S. Khare, A note on fuzzy subgroups and fuzzy homomorphism, J. Math. Anal. Appl., 131 (1988), 537-553. doi: 10.1016/0022-247X(88)90224-7
[7]	V. N. Dixit, R. Kumar, N. Ajmal, Level subgroups and union of fuzzy subgroups, Fuzzy Set. Syst., 37 (1990), 359-371. doi: 10.1016/0165-0114(90)90032-2
[8]	R. Biswas, Fuzzy subgroups and anti-fuzzy subgroups, Fuzzy Set. Syst., 35 (1990), 121-124. doi: 10.1016/0165-0114(90)90025-2
[9]	N. Ajmal, A. S. Prajapati, Fuzzy cosets and fuzzy normal subgroups, Inform. Sciences, 64 (1992), 17-25. doi: 10.1016/0020-0255(92)90107-J
[10]	A. B. Chakraborty, S. S. Khare, Fuzzy homomorphism and algebraic structures, Fuzzy Set. Syst., 59 (1993), 211-221. doi: 10.1016/0165-0114(93)90201-R
[11]	N. P. Mukherjee, P. Bhattacharya, Fuzzy normal subgroups and fuzzy cosets, Inform. Sciences, 34 (1984), 225-239. doi: 10.1016/0020-0255(84)90050-1
[12]	N. P. Mukherjee, P. Bhattacharya, Fuzzy groups: some group-theoretic analogs, Inform. Sciences, 39 (1986), 247-267. doi: 10.1016/0020-0255(86)90039-3
[13]	P. Bhattacharya, Fuzzy subgroups: some characterizations. II, Inform. Sciences, 38 (1986), 293-297. doi: 10.1016/0020-0255(86)90028-9
[14]	M. Tarnauceanu, Classifying fuzzy normal subgroups of finite groups, Iran. J. Fuzzy Syst., 12 (2015), 107-115.
[15]	B. O. Onasanya, Review of some anti fuzzy properties of some fuzzy subgroups, Anal. Fuzzy Math. Inform., 11 (2016), 899-904.
[16]	U. Shuaib, M. Shaheryar, W. Asghar, On some characterizations of o-fuzzy subgroups, IJMCS, 13 (2018), 119-131.
[17]	U. Shuaib, M. Shaheryar, On some properties of o-anti fuzzy subgroups, IJMCS, 14 (2019), 215-230.
[18]	G. M. Addis, Fuzzy homomorphism theorems on groups, Korean J. Math., 26 (2018), 373-385.
[19]	K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Set. Syst., 20 (1986), 87-96.
[20]	R. Biswas, Intuitionistic fuzzy subgroup, Mathematical Forum, 10 (1989), 39-44.
[21]	J. Zhan, Z. Tan, Intuitionistic M-fuzzy groups, Soochow J. Math., 30 (2004), 85-90.
[22]	S. Bhunia, G. Ghorai, A new approach to fuzzy group theory using (α, β)-pythagorean fuzzy sets, Song. J. Sci. Tech., In press.
[23]	R. A. Husban, A. R. Salleh, A. G. Ahmad, Complex intuitionistic fuzzy normal subgroup, IJPAM, 115 (2017), 199-210.
[24]	A. Solairaju, S. Mahalakshmi, Hesitant intuitionistic fuzzy soft groups, IJMCS, 118 (2018), 223-232.
[25]	R. R. Yager, Pythagorean fuzzy subsets, In: 2013 Joint IFSA World Congress and NAFIPS Annual Meeting (IFSA/NAFIPS), 2013, 36286152.
[26]	S. Naz, S. Ashraf, M. Akram, A novel approach to decision-making with Pythagorean fuzzy information, Mathematics, 6 (2018), 1-28.
[27]	M. Akram, S. Naz, A novel decision-making approach under complex pythagorean fuzzy environment, Math. Comput. Appl., 24 (2019), 1-33.
[28]	P. A. Ejegwa, Pythagorean fuzzy set and its applications in career placements based on academics performance using max-min-max composition, Complex Intell. Syst., 5 (2019), 165-175. doi: 10.1007/s40747-019-0091-6
[29]	X. Peng, Y. Yang, Some results for Pythagorean fuzzy sets, Int. J. Intell. Syst., 30 (2015), 1133-1160. doi: 10.1002/int.21738
[30]	X. Peng, Y. Yang, Fundamental properties of interval-valued Pythagorean fuzzy aggregation operators, Int. J. Intell. Syst., 31 (2016), 444-487. doi: 10.1002/int.21790
[31]	R. R. Yager, Properties and application of Pythagorean fuzzy sets, In: Imprecision and uncertainty in information representation and processing, Cham: Springer, 2016,119-136.

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