On Certain Properties of the $\beta$-Flexible Q-Fuzzy Groups and $\beta$-Flexible Normal Q-Fuzzy Subgroups

# Geethalakshmi Manickam1

1Department of General Requirements, Nizwa College of Applied Sciences, University of Technology and Applied Sciences, Sultanate of Oman.

Abstract: The main purpose of this study is to introduce the new concept of fuzzy set and $\beta$-flexible fuzzy set. Based on this, the concept of $\beta$-flexible Q-fuzzy group and $\beta$-flexible normal Q-fuzzy subgroups are given. The necessary properties related to these two concepts are discussed and proved by using these definitions. We shall also extend some new results related to this subject.
Keywords: Fuzzy set, $\beta$-flexible fuzzy subset, $\beta$-flexible Q-fuzzy subset, $\beta$-flexible Q-fuzzy group and $\beta$-flexible Q-fuzzy normal subgroups.

Cite this article as: Geethalakshmi Manickam, On Certain Properties of the $\beta$-Flexible Q-Fuzzy Groups and $\beta$-Flexible Normal Q-Fuzzy Subgroups, Int. J. Math. And Appl., vol. 10, no. 1, 2022, pp. 111-117.

References
1. A. Rosenfield, Fuzzy groups, J. Math. Anal. Appl., 35(1965), 521-517.
2. J. H. Anthony and H. Sherwood, Fuzzy groups redefined, J. Hath. Anal. Appl., 69(1979), 124-130.
3. N. P. Mukherjee and P. Bhattacharya, Fuzzy normal subgroups and fuzzy cosets, Information Sciences, 34(1984), 225-239.
4. N. P. Mukherjee and P. Bhattacharya, Fuzzy groups: Some group theoretic analogs, Information Sciences, 39(1986), 247-269.
5. V. Murali and B. B. Makamba, Fuzzy subgroups of finite abelian groups, Far East journal of Mathematical Science, 14(2004), 360-371.
6. V. Murali and B. B. Makamba, Counting the number of fuzzy subgroups of on abelian group of order $p^{n }q$, Fuzzy sets and systems, 44(2006), 459-470.
7. A. Solairaju and R. Nagarajan, Q-fuzzy left R-subgroup of near rings with respect to T-norms, Antarctica Journal of Mathematics, 5(1-2)(2008), 59-63.
8. A. Solairaju and R. Nagarajan, A new structure and construction of Q-fuzzy groups, Advances in Fuzzy Mathematics, 4(1)(2009), 23-29.
9. A. Zadeh, Fuzzy Sets, Information and Control, 8(1965), 338-353.
10. A. Solairaju and R. Nagarajan, Some structure properties of upper Q-fuzzy index order with upper Q-fuzzy subgroups, Int. Journal of open Problem Math. Appl., 1(2011), 21-29.
11. P. Sarangapani and P. Muruganantham, New structures on upper flexible Q-fuzzy groups, International Journal of Mathematics Research, 8(2)(2016), 107-112.
12. W. H. Wu, Normal fuzzy subgroups, Fuzzy Math., 1(1981), 21-30.
13. M. Massadeh, Properties of fuzzy subgroups in particular the normal subgroups, Doctorate Thesis, Damacus University-Syrian Arab Republic.
14. V. Vanitha and G. Subbiah, Certain thresholds on flexible fuzzy subgroups with flexible fuzzy order, Int. Rearch Journal of Pure Algebra, 6(11)(2016), 436-442.
15. H. J. Zimmerman, Fuzzy set theory and its applications, Third Edition, Kluwer Academic publishers London, (1997).
16. Muhammad Gulzar and Ghazanfar Abbas, Algebraic Properties of $\omega$-Q-fuzzy subgroups, Int. Journal of Mathematics and Computer Science, 15(1)(2020), 265-274.
17. Geethalakshmi Manickam and A. Solairaju, New structure properties of flexible Q-fuzzy groups and flexible normal Q-fuzzy subgroups, Int. Research Journal of Pure Algebra, 10(7)(2020), 14-18.

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