On smallest (generalized) ideals and semilattices of (2,2)-regular non-associative ordered semigroups
Resumen
An ordered AG-groupoid can be referred to as a non-associative ordered semigroup, as the main di¤erence between an ordered semigroup and an ordered AG-groupoid is the switching of an associative law. In this paper, we dene the smallest left (right) ideals in an ordered AG-groupoid and use them to characterize a (2; 2)-regular class of a unitary ordered AG-groupoid along with its semilattices and (2 ;2 _q)-fuzzy left (right) ideals. We also give the concept of an ordered A*G**-groupoid and investigate its structural properties by using the generated ideals and (2 ;2 _q)-fuzzy left (right) ideals. These concepts will verify the existing characterizations and will help in achieving more generalized results in future works.
Descargas
Citas
S. K Bhakat and P.Das, On the definition of a fuzzy subgroups, Fuzzy sets Syst., 51(1992), 235-241. DOI: https://doi.org/10.1016/0165-0114(92)90196-B
B. Davvaz, (∈,∈ ∨q)-fuzzy subnear-rings and ideals, Soft Computing, 10(2006), 206-211. DOI: https://doi.org/10.1007/s00500-005-0472-1
W. A. Dudek and R. S. Gigon, Congruences on completely inve rse AG**-groupoids, Quasigroups and related systems, 20 (2012), 203-209.
W. A. Dudek and R. S. Gigon, Completely inverse AG**-group oids. Semigroup Forum, 87 (2013), 201-229. DOI: https://doi.org/10.1007/s00233-013-9465-z
O. Kazanci and S. Yamak, Generalized fuzzy bi-ideals of semigroup, Soft Comput., 12(2008), 1119-1124. DOI: https://doi.org/10.1007/s00500-008-0280-5
M. A. Kazim and M. Naseeruddin, On almost semigroups, The A lig. Bull. Math., 2(1972), 1-7.
M. Khan, Some studies in AG*-groupoids, Ph. D Thesis, Quaid-i-Azam University, Pakistan, 2008.
V. Murali, Fuzzy points of equivalent fuzzy subsets, Inform. Sci., 158 (2004) 277−288. DOI: https://doi.org/10.1016/j.ins.2003.07.008
Q. Mushtaq and S. M. Yusuf, On LA-semigroups, The Alig. Bull. Math., 8(1978), 65-70.
Q. Mushtaq and S. M. Yusuf, On locally associative left al most semigroups, J. Nat. Sci. Math., 19(1979), 57-62.
V. Protic and N. Stevanovic, AG-test and some general properties of Abel-Grassmann’s groupoids, PU. M. A., 4, 6 (1995), 371-383.
P.M. Pu and Y.M. Liu, Fuzzy topology I, neighborhood structure of a fuzzy point and Moore Smith convergence, J. Math. Anal. Appl., 76 (1980) 571−599. DOI: https://doi.org/10.1016/0022-247X(80)90048-7
A. Rosenfeld, Fuzzy groups, J. Math. Anal, Appl., 35(1971), 512-517. DOI: https://doi.org/10.1016/0022-247X(71)90199-5
N. Stevanovic and P. V. Protic, Composition of Abel-Grassmann’s 3-bands, Novi Sad, J. Math., 2, 34 (2004), 175-182.
M. Shabir, Y. B. Junan Y. Nawaz, Characterizations of regular semigroups by (α, β)-fuzzy ideals, Computers and Mathematics with Applications, 59(2010), 161-175. DOI: https://doi.org/10.1016/j.camwa.2009.06.014
M. Shabir, Y. B. Junan Y. Nawaz, Semigroups charactarized by (∈,∈ ∨qk)-fuzzy ideals, Computer and Mathematics with applications, 60(2010), 1473-1493. DOI: https://doi.org/10.1016/j.camwa.2010.06.030
F. Yousafzai, A. Khan, V. Amjid and A. Zeb, On fuzzy fully regular ordered AG-groupoids, Journal of Intelligent & Fuzzy Systems, 26 (2014), 2973-2982.
F. Yousafzai, N. Yaqoob and A. Zeb, On generalized fuzzy ideals of ordered AG-groupoids, International Journal of Machine Learning and Cybernetics, 7 (2016), 995-104. DOI: https://doi.org/10.1007/s13042-014-0305-6
L. A.Zadeh, Fuzzy sets, Information and Control., 8(1965), 338-353. DOI: https://doi.org/10.1016/S0019-9958(65)90241-X
Derechos de autor 2021 Boletim da Sociedade Paranaense de Matemática
Esta obra está bajo licencia internacional Creative Commons Reconocimiento 4.0.
When the manuscript is accepted for publication, the authors agree automatically to transfer the copyright to the (SPM).
The journal utilize the Creative Common Attribution (CC-BY 4.0).
Funding data
