Characterizing semi-groups through the properties of their fuzzy \(m\)-bi-ideals
Volume 23, Issue 3, pp 170--180
http://dx.doi.org/10.22436/jmcs.023.03.01
Publication Date: November 01, 2020
Submission Date: August 26, 2020
Revision Date: September 08, 2020
Accteptance Date: September 24, 2020
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Authors
Mohammad Munir
- Department of Mathematics, Government Postgraduate College, Abbottabad, Pakistan.
Nasreen Kausar
- Department of Mathematics and Statistics, University of Agriculture, Faisalabad, Pakistan.
Salahuddin
- Department of Mathematics, Jazan University, Jazan, Kingdom of Saudi Arabia.
Anum Shafiq
- School of Mathematics and Statistics, Nanjing University of Information Science and Technology, Nanjing 210044, China.
Mustafa Habib
- Department of Mathematics, University of Engineering and Technology, Lahore, Pakistan.
Abstract
In this article, we present the idea of the fuzzy \(m\)-bi-ideals in semi-groups and describe their basic algebraic properties. We also develop the forms of the fuzzy \(m\)-bi-ideals generated by an element, a subset, and a sub-semi-group of the semi-group. Important characterizations of semi-groups and their different types like \(m\)-regular semi-groups and \(m\)-intraregular semi-groups have been given through demonstrating examples and using properties of fuzzy \(m\)-bi-ideals in semi-groups.
Share and Cite
ISRP Style
Mohammad Munir, Nasreen Kausar, Salahuddin, Anum Shafiq, Mustafa Habib, Characterizing semi-groups through the properties of their fuzzy \(m\)-bi-ideals, Journal of Mathematics and Computer Science, 23 (2021), no. 3, 170--180
AMA Style
Munir Mohammad, Kausar Nasreen, Salahuddin, Shafiq Anum, Habib Mustafa, Characterizing semi-groups through the properties of their fuzzy \(m\)-bi-ideals. J Math Comput SCI-JM. (2021); 23(3):170--180
Chicago/Turabian Style
Munir, Mohammad, Kausar, Nasreen, , Salahuddin, Shafiq, Anum, Habib, Mustafa. "Characterizing semi-groups through the properties of their fuzzy \(m\)-bi-ideals." Journal of Mathematics and Computer Science, 23, no. 3 (2021): 170--180
Keywords
- Bipotency
- Fuzzy \(m\)-points
- \(m\)-regular semi-groups
- \(m\)-intraregular semi-groups
MSC
References
-
[1]
J. Ahsan, R. M. Latif, M. Shabir, Fuzzy quasi-ideals in semigroups, J. Fuzzy Math., 9 (2001), 259--270
-
[2]
I. Chon, On fuzzy bi-ideals in semigroups, Korean J. Math., 19 (2011), 321--330
-
[3]
R. Good, D. Hughes, Associated groups for a semigroup, in: Bull. Amer. Math. Soc., 58 (1952), 624--625
-
[4]
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
-
[5]
R. Kumar, Fuzzy semiprimary ideals of rings, Fuzzy Sets and Systems, 42 (1991), 263--272
-
[6]
W. J. Liu, Fuzzy invariant subgroups and fuzzy ideals, Fuzzy sets and Systems, 8 (1982), 133--139
-
[7]
W.-J. Liu, Operations on fuzzy ideals, Fuzzy Sets and Systems, 11 (1983), 31--41
-
[8]
J. N. Mordeson, D. S. Malik, Fuzzy automata and languages: theory and applications, Chapman & Hall/CRC, Boca Raton (2002)
-
[9]
J. N. Mordeson, D. S. Malik, N. Kuroki, Fuzzy semigroups, Springer-Verlag, Berlin (2012)
-
[10]
T. K. Mukherjee, M. K. Sen, On fuzzy ideals of a ring I, Fuzzy Sets and Systems, 21 (1987), 99--104
-
[11]
M. Munir, On $m$-bi ideals in semigroups, Bull. Int. Math. Virtual Inst., 8 (2018), 461--467
-
[12]
M. Munir, A. Ali, On generalization of quasi ideals in semirings, Bull. Int. Math. Virtual Inst., 10 (2020), 83--94
-
[13]
M. Munir, A. Shafiq, A generalization of bi ideals in semirings, Bull. Int. Math. Virtual Inst., 8 (2018), 123--133
-
[14]
W. Nakkhasen, B. Pibaljommee, On $m$-bi-hyperideals in semihyperrings, Songklanakarin J. Sci. Technol., 41 (2019), 1241--1247
-
[15]
M. M. K. Rao, Fuzzy bi-interior ideals of semigroups, Asia Pacific. J. Math., 5 (2018), 208--218
-
[16]
R. Rasuli, $T$-fuzzy bi-ideals in semirings, Earthline J. Math. Sci., 2 (2019), 241--263
-
[17]
M. Shabir, Y. B. Jun, M. Bano, On prime fuzzy bi-ideals of semigroups, Iran. J. Fuzzy Syst., 7 (2010), 115--128
-
[18]
M. Shabir, Y. Nawaz, M. Aslam, Semigroups characterized by the properties of their fuzzy ideals with thresholds, World Appl. Sci. J., 14 (2011), 1851--1865
-
[19]
T. Shah, N. Kausar, Characterizations of non-associative ordered semigroups by their fuzzy bi-ideals, Theoret. Comput. Sci., 529 (2014), 96--110
-
[20]
U. M. Swamy, K. L. N. Swamy, Fuzzy prime ideals of rings, J. Math. Anal. Appl., 134 (1988), 94--103
-
[21]
X.-Y. Xie, Fuzzy ideals in semigroups, J. Fuzzy Math., 7 (1999), 357--365
-
[22]
L. A. Zadeh, Fuzzy sets, Inf. Control, 8 (1965), 338--353
-
[23]
Y. Zhang, Prime $L$-fuzzy ideals and primary $L$-fuzzy ideals, Fuzzy Sets and Systems, 27 (1988), 345--350
-
[24]
H. Zimmermann, Fuzzy sets theory and its application, Kluwer Academic Publ., New York (2001)