[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.11568/kjm.2020.28.3.623

A CHARACTERIZATION OF SEMIGROUPS THROUGH THEIR FUZZY GENERALIZED m-BI-IDEALS

Munir, Mohammad (Department of Mathematics, Government Postgraduate College)
Kausar, Nasreen (Department of Mathematics, Agriculture University)
Anjum, Rukhshanda (Department of Mathematics and Statistics, University of Lahore)
Ali, Asghar (Department of Mathematics Mirpur University of science and Technology (MUST))
Hussain, Rashida (Department of Mathematics Mirpur University of science and Technology (MUST))

Publication Information

Korean Journal of Mathematics / v.28, no.3, 2020 , pp. 623-638 More about this Journal

Abstract

In this article, we initially present the concept of the fuzzy generalized m-bi-ideals in semigroups, then making use of their important types like prime, semiprime and strongly fuzzy generalized m-bi-ideals, we give the important characterizations of the semigroups. We also characterize the m-regular and m-intraregular semigroups using the properties of the irreducible and strongly irreducible fuzyy generalized m-bi-ideals.

Keywords

Fuzzy generalized m-bi-ideals; Strongly prime generalized m-bi-ideals; Semiprime generalized m-bi-ideals;

Citations & Related Records

Reference

1	J. Ahsan, R. Latif, and M. Shabir, Fuzzy quasi-ideals in semigroups, J. Fuzzy Math. 9 (2) (2001), 259-270.
2	F.M. Khan, N.H. Sarmin, and H.A. Khan, A novel approach towards fuzzy generalized bi-ideals in ordered semigroups, The Sci. World J. Article ID 275947, (2014), 1-9.
3	N. Kausar, Characterizations of non associative ordered semigroups by the properties of their fuzzy ideals with thresholds ( ${\alpha}$ , ${\beta}$ ], Prikladnaya Diskretnaya Matematika 43 (1), (2019), 37-59.
4	N. Kausar, A. Meshari, and Salahuddin, Anti fuzzy interior ideals on Ordered AG-groupoids, Eur. J. Pur. Appl. Math.13 (1), (2020), 113-129. DOI
5	N. Kausar, M. Alesemi, Salahuddin, and M. Munir, Characterizations of non-associative ordered semigroups by their intuitionistic fuzzy bi-ideals, Disc. Nonlin. Compl. 9 (2)(2020), 257-275.
6	N. Kuroki, On fuzzy semigroups, Inform. Sci. 53 (3) (1991), 203-236. DOI
7	J. N. Mordeson, D.S. Malik, and N. Kuroki, Fuzzy semigroups, 131, Springer.
8	M. Munir, and M. Habib, Characterizing semirings using their quasi and bi-ideals, Proc. Pakistan Acad. Sci. 53 (4), (2016), 469-475.
9	M. Munir, On m-bi ideals in semigroups, Bull. Int. Math. Virt. Inst. 8 (3), (2018), 461-467.
10	M. Munir, and A. Shafiq, A generalization of Bi ideals in semirings, Bull. Int. Math. Virt. Inst. 8 (1), (2018), 123-33.
11	M. Munir, A. Asghar, On generalization of quasi ideals in semirings. Bull. Int. Math. Virt. Inst. 10 (2020), 83-94.
12	M. Munir, N. Kausar, Salahuddin, and Tehreem, On the prime fuzzy m-bi ideals in semigroups, J. Math. Comp. Sci. 21 (4) (2020), 357-365. DOI
13	M.M.K. Rao, Fuzzy bi-interior ideals of semigroups, Asia Pac. J. Math. 5 (2) (2018), 208-218.
14	M. Shabir, Y. B. Jun, and M. Bano, On prime fuzzy bi-ideals of semigroups, Iran. J. of Fuzz. Syst. 7 (3) (2010), 115-128.
15	T. Shah, N. Kausar, Characterizations of non-associative ordered semigroups by their fuzzy bi-ideals, Theor. Comp. Sci. 529 (2014), 96-110. DOI
16	L.A. Zadeh, Fuzzy sets Inform. cont. 8 (3) (1965), 338-353. DOI