Research article

On the characterization of Pythagorean fuzzy subgroups

  • 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.

    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

    Related Papers:

  • 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.


    加载中


    [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.
  • Reader Comments
  • © 2021 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(3780) PDF downloads(294) Cited by(10)

Article outline

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog