On the prime fuzzy \(m\)-bi ideals in semigroups
- Government Postgraduate College, Abbottabad, Pakistan.
- Department of Mathematics, University of Agriculture, Faisalabad, Pakistan.
- Department of Mathematics, Jazan University, Jazan, Kingdom of Saudi Arabia.
- Department of Mathematics, Air University (AU), Islamabad, Pakistan.
In this article, we build up the ideas of the fuzzy strongly prime, prime and semiprime \(m\)-bi ideals in a semigroup. We additionally investigate the conditions that when the fuzzy \(m\)-bi ideals are irreducible and strongly irreducible. We have demonstrated that a semigroup is \(m\)-regular and \(m\)-intraregular if and only if its very fuzzy \(m\)-bi ideal is a semiprime, likewise a subset of a semigroup is its \(m\)-bi ideal if and only if the characteristic function on this subset is a fuzzy \(m\)-bi ideal.
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Mohammad Munir, Nasreen Kausar, Salahuddin, Tehreem, On the prime fuzzy \(m\)-bi ideals in semigroups, Journal of Mathematics and Computer Science, 21 (2020), no. 4, 357--365
Munir Mohammad, Kausar Nasreen, Salahuddin, Tehreem, On the prime fuzzy \(m\)-bi ideals in semigroups. J Math Comput SCI-JM. (2020); 21(4):357--365
Munir, Mohammad, Kausar, Nasreen, , Salahuddin, , Tehreem. "On the prime fuzzy \(m\)-bi ideals in semigroups." Journal of Mathematics and Computer Science, 21, no. 4 (2020): 357--365
- Fuzzy \(m\)-bi ideals
- strongly prime \(m\)-bi ideals
- semiprime \(m\)-bi ideals
J. Ahsan, R. M. Latif, M. Shabir, Fuzzy quasi-ideals in semigroups, J. Fuzzy Math., 9 (2001), 259--270
J. S. Golan, The theory of semirings with applications in mathematics and theoretical computer science, John Wiley & Sons, New York (1992)
J. M. Howie, An introduction to semigroup theory, Academic Press, New York-London (1976)
N. Kausar, Characterizations of non associative ordered semigroups by the properties of their fuzzy ideals with thresholds ($\alpha$, $\beta$], Prikl. Diskretn. Mat., 43 (2019), 37--59
N. Kausar, A. Meshari, Salahuddin, Anti fuzzy interior ideals on Ordered AG-groupoids, Eur. J. Pure Appl. Math., 13 (2020), 113--129
N. Kausar, A. Meshari Alesemi, Salahuddin, M. Munir, Characterizations of non-associative ordered semigroups by their intuitionistic fuzzy bi-ideals, Disc. Nonl. Compl., 9 (2020), 257--275
N. Kuroki, On fuzzy ideals and fuzzy bi-ideals in semigroups, Fuzzy Sets and Systems, 5 (1981), 203--215
J. N. Mordeson, D. S. Malik, N. Kuroki, Fuzzy semigroups, Springer-Verlag, Berlin (2012)
J. N. Mordeson, P. S. Nair, Fuzzy Graphs and Fuzzy Hypergraphs, Physica-Verlag, Heidelberg (2000)
M. Munir, On $m$-bi ideals in semigroups, Bull. Int. Math. Virtual Inst., 8 (2018), 461--467
M. M. K. Rao, Fuzzy bi-interior ideals of semigroups, Asia Pacific. J. Math., 5 (2018), 208--218
M. Shabir, Y. B. Jun, M. Bano, On prime fuzzy bi-ideals of semigroups, Iran. J. Fuzzy Syst., 7 (2010), 115--128
T. Shah, N. Kausar, Characterizations of non-associative ordered semigroups by their fuzzy bi-ideals, Theoret. Comput. Sci., 529 (2014), 96--110
L. A. Zadeh, Fuzzy set, Information and Control, 338--353 (1965),
H. Zimmermann, Fuzzy sets theory and its application, Kluwer Academic Publ., New York (2001)