# Some results in bipolar-valued fuzzy ordered AG-groupoids

Faisal; Naveed Yaqoob; Arsham Borumand Saeid

Discussiones Mathematicae - General Algebra and Applications (2012)

- Volume: 32, Issue: 1, page 55-76
- ISSN: 1509-9415

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topFaisal, Naveed Yaqoob, and Arsham Borumand Saeid. "Some results in bipolar-valued fuzzy ordered AG-groupoids." Discussiones Mathematicae - General Algebra and Applications 32.1 (2012): 55-76. <http://eudml.org/doc/270595>.

@article{Faisal2012,

abstract = {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.},

author = {Faisal, Naveed Yaqoob, Arsham Borumand Saeid},

journal = {Discussiones Mathematicae - General Algebra and Applications},

keywords = {Ordered AG-groupoid; intra-regular ordered AG-groupoid; bipolar-valued fuzzy two-sided ideal; (strong) negative s-cut; (strong) positive t-cut; ordered -groupoids; bipolar-valued fuzzy two-sided ideals},

language = {eng},

number = {1},

pages = {55-76},

title = {Some results in bipolar-valued fuzzy ordered AG-groupoids},

url = {http://eudml.org/doc/270595},

volume = {32},

year = {2012},

}

TY - JOUR

AU - Faisal

AU - Naveed Yaqoob

AU - Arsham Borumand Saeid

TI - Some results in bipolar-valued fuzzy ordered AG-groupoids

JO - Discussiones Mathematicae - General Algebra and Applications

PY - 2012

VL - 32

IS - 1

SP - 55

EP - 76

AB - 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.

LA - eng

KW - Ordered AG-groupoid; intra-regular ordered AG-groupoid; bipolar-valued fuzzy two-sided ideal; (strong) negative s-cut; (strong) positive t-cut; ordered -groupoids; bipolar-valued fuzzy two-sided ideals

UR - http://eudml.org/doc/270595

ER -

## References

top- [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. Zbl1301.20074
- [2] M. Aslam, S. Abdullah and M. Maqsood, Bipolar fuzzy ideals in LA-semigroups, World Appl. Sci. J. 17 (12) (2012), 1769-1782.
- [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. Zbl1309.20061
- [4] A. Borumand Saeid, Bipolar-valued fuzzy BCK/BCI-algebras, World Appl. Sci. J. 7 (11) (2009), 1404-1411.
- [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 Zbl1304.20081
- [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. Zbl1274.20108
- [7] P. Holgate, Groupoids satisfying a simple invertive law, The Math. Stud. 61 (1992), 101-106. Zbl0900.20160
- [8] M.A. Kazim and M. Naseeruddin, On almost semigroups, Aligarh Bull. Math. 2 (1972), 1-7.
- [9] M. Khan and Faisal, On fuzzy ordered Abel-Grassmann's groupoids, J. Math. Res. 3 (2011), 27-40.
- [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.
- [11] N. Kuroki, Fuzzy bi-ideals in semigroups, Comment. Math. Univ. St. Pauli 27 (1979), 17-21. Zbl0428.20041
- [12] K.M. Lee, Bi-polar-valued fuzzy sets and their operations, Proc. Int. Conf. Intel. Tech. Bangkok Thailand (2000), 307-312.
- [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
- [14] Q. Mushtaq and S.M. Yusuf, On LA-semigroups, Aligarh. Bull. Math. 8 (1978), 65-70.
- [15] Q. Mushtaq and S.M. Yusuf, On LA-semigroup defined by a commutative inverse semigroups, Math. Bech. 40 (1988), 59-62. Zbl0692.20053
- [16] M. Naseeruddin, Some studies in almost semigroups and flocks, Ph.D., thesis. Aligarh Muslim University, Aligarh, India, 1970.
- [17] A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl. 35 (1971), 512-517. doi: 10.1016/0022-247X(71)90199-5
- [18] N. Stevanović and P.V. Protić, Composition of Abel-Grassmann's 3-bands, Novi Sad J. Math. 2 (34) (2004), 175-182. Zbl1060.20056
- [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. Zbl1159.06009
- [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.
- [21] N. Yaqoob, Bipolar-valued fuzzy ideals in LA-semigroups, J. Adv. Stud. Topol. 3 (1) (2012), 60-71. Zbl1330.20087
- [22] N. Yaqoob and M. Aslam, Yao's generalized rough approximations in left almost semigroups, Ann. Fuzzy Math. Inform. 3 (1) (2012), 119-131. Zbl1301.20090
- [23] N. Yaqoob, Interval-valued intuitionistic fuzzy ideals of regular LA-semigroups, Thai J. Math. (in press). Zbl1291.20067
- [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 Zbl1279.20086
- [25] L.A. Zadeh, Fuzzy sets, Inform. Control. 8 (1965), 338-353. doi: 10.1016/S0019-9958(65)90241-X Zbl0139.24606

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