In this paper, we introduce the concept of bipolar-valued fuzzification of ordered 𝓐𝓖-groupoids and discuss some structural properties of bipolar-valued fuzzy two-sided ideals of an intra-regular ordered 𝓐𝓖-groupoid.
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1186, author = {Faisal and Naveed Yaqoob and Arsham Borumand Saeid}, title = {Some results in bipolar-valued fuzzy ordered AG-groupoids}, journal = {Discussiones Mathematicae - General Algebra and Applications}, volume = {32}, year = {2012}, pages = {55-76}, zbl = {1305.06011}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1186} }
Faisal; Naveed Yaqoob; Arsham Borumand Saeid. Some results in bipolar-valued fuzzy ordered AG-groupoids. Discussiones Mathematicae - General Algebra and Applications, Tome 32 (2012) pp. 55-76. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmal_1186/
[000] [1] S. Abdullah, M. Aslam, N. Amin and T. Khan, Direct product of finite fuzzy subsets of LA-semigroups, Ann. Fuzzy Math. Inform. 3 (2) (2012), 281-292. | Zbl 1301.20074
[001] [2] M. Aslam, S. Abdullah and M. Maqsood, Bipolar fuzzy ideals in LA-semigroups, World Appl. Sci. J. 17 (12) (2012), 1769-1782.
[002] [3] M. Aslam, S. Abdullah and N. Amin, Characterization of Γ-LA-semigroups by generalized fuzzy Γ-ideals, Int. J. Math. Stat. 11 (1) (2012), 29-50. | Zbl 1309.20061
[003] [4] A. Borumand Saeid, Bipolar-valued fuzzy BCK/BCI-algebras, World Appl. Sci. J. 7 (11) (2009), 1404-1411.
[004] [5] Faisal, N. Yaqoob and A. Ghareeb, Left regular AG-groupoids in terms of fuzzy interior ideals, Afr. Mat. (in press). doi: 10.1007/s13370-012-0081-y | Zbl 1304.20081
[005] [6] Faisal, N. Yaqoob and K. Hila, On fuzzy (2,2)-regular ordered Γ-AG**-groupoids, U.P.B. Sci. Bull. Ser. A 74 (2) (2012), 87-104. | Zbl 1274.20108
[006] [7] P. Holgate, Groupoids satisfying a simple invertive law, The Math. Stud. 61 (1992), 101-106. | Zbl 0900.20160
[007] [8] M.A. Kazim and M. Naseeruddin, On almost semigroups, Aligarh Bull. Math. 2 (1972), 1-7.
[008] [9] M. Khan and Faisal, On fuzzy ordered Abel-Grassmann's groupoids, J. Math. Res. 3 (2011), 27-40.
[009] [10] M. Khan and Faisal, Intra-regular AG-groupoids characterized by their intuitionistic fuzzy ideals, J. Adv. Res. Dyn. Control. Syst. 2 (2011), 17-33.
[010] [11] N. Kuroki, Fuzzy bi-ideals in semigroups, Comment. Math. Univ. St. Pauli 27 (1979), 17-21. | Zbl 0428.20041
[011] [12] K.M. Lee, Bi-polar-valued fuzzy sets and their operations, Proc. Int. Conf. Intel. Tech. Bangkok Thailand (2000), 307-312.
[012] [13] K.M. Lee, Comparison of interval-valued fuzzy sets, intuitionistic fuzzy sets and bipolar-valued fuzzy sets, J. Korean Inst. Intel. Syst. 14 (2) (2004), 125-129. doi: 10.5391/JKIIS.2004.14.2.125
[013] [14] Q. Mushtaq and S.M. Yusuf, On LA-semigroups, Aligarh. Bull. Math. 8 (1978), 65-70.
[014] [15] Q. Mushtaq and S.M. Yusuf, On LA-semigroup defined by a commutative inverse semigroups, Math. Bech. 40 (1988), 59-62. | Zbl 0692.20053
[015] [16] M. Naseeruddin, Some studies in almost semigroups and flocks, Ph.D., thesis. Aligarh Muslim University, Aligarh, India, 1970.
[016] [17] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl. 35 (1971), 512-517. doi: 10.1016/0022-247X(71)90199-5
[017] [18] N. Stevanović and P.V. Protić, Composition of Abel-Grassmann's 3-bands, Novi Sad J. Math. 2 (34) (2004), 175-182. | Zbl 1060.20056
[018] [19] X.Y. Xie and J. Tang, Fuzzy radicals and prime fuzzy ideals of ordered semigroups, Inform. Sci. 178 (2008), 4357-4374. doi:10.1016/j.ins.2008.07.006. | Zbl 1159.06009
[019] [20] N. Yaqoob, S. Abdullah, N. Rehman and M. Naeem, Roughness and fuzziness in ordered ternary semigroups, World Appl. Sci. J. 17 (12) (2012), 1683-1693.
[020] [21] N. Yaqoob, Bipolar-valued fuzzy ideals in LA-semigroups, J. Adv. Stud. Topol. 3 (1) (2012), 60-71. | Zbl 1330.20087
[021] [22] N. Yaqoob and M. Aslam, Yao's generalized rough approximations in left almost semigroups, Ann. Fuzzy Math. Inform. 3 (1) (2012), 119-131. | Zbl 1301.20090
[022] [23] N. Yaqoob, Interval-valued intuitionistic fuzzy ideals of regular LA-semigroups, Thai J. Math. (in press). | Zbl 1291.20067
[023] [24] N. Yaqoob, R. Chinram, A. Ghareeb and M. Aslam, Left almost semigroups characterized by their interval valued fuzzy ideals, Afr. Mat. (in press). doi: 10.1007/s13370-011-0055-5 | Zbl 1279.20086
[024] [25] L.A. Zadeh, Fuzzy sets, Inform. Control. 8 (1965), 338-353. doi: 10.1016/S0019-9958(65)90241-X | Zbl 0139.24606