Faiz Muhammad Khan, Nie Yufeng, Madad Khan, Weiwei Zhang

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Based on generalized quasi-coincident with relation, new types of fuzzy bi-ideals of an ordered semigroup S are introduced. Level subset and characteristic functions are used to linked ordinary bi-ideals and (2;2_(|;qk))fuzzy bi-ideals of an ordered semigroup S: Further, upper/lower parts of (2;2 _(|;qk))-fuzzy bi-ideals of S are determined. Finally, some well known classes of ordered semigroups like regular, left (resp. right) regular and completely regular ordered semigroups are characterized by the properties of (2;2_(|;qk))-fuzzy bi-ideals.


fuzzy bi-ideals; ordered semigroup; level subset; characteristic functions.

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S. K. Bhakat and P. Das, (∈,∈ ∨q)-fuzzy subgroups, Fuzzy Sets and Systems 80 (1996) , 359-368.

S. K. Bhakat and P. Das, Fuzzy subrings and ideals redefined, Fuzzy Sets and Systems, 81 (1996),383 − 393.

B. Davvaz and M. Mozafar, (∈,∈ ∨q)-fuzzy Lie subalgebra and ideals, International Journal of Fuzzy Systems, 11(2)(2009) 123-129.

B. Davvaz, Fuzzy R-subgroups with thresholds of near-rings and implication operators, Soft Computing, 12 (2008) 875-879.

B. Davvaz, (∈,∈ ∨q)-fuzzy subnearrings and ideals, Soft Comput, 10 (2006) ,206−211.

B. Davvaz and P. Corsini, On (α,β)-fuzzy H v -ideals of H v -rings, Iran. J.Fuzzy Syst. 5 (2008), No. 2, 35-47.

Y. B. Jun, A. Khan and M. Shabir, Ordered semigroups characterized by their (∈,∈ ∨q)-fuzzy bi-ideals, Bull. Malays. Math. Sci. Soc. (2) 32(3) (2009), 391–408.

Y. B. Jun, Generalizations of (∈,∈ ∨q)-fuzzy subalgebras in BCK/BCI-algebras. Computers and Mathematics with Applications. 2009. 58: 13831390.

Y. B. Jun, M. A., Ozturk and G. Muhiuddin, A generalization of (∈,∈ ∨q)-fuzzy subgroups International Journal of Algebra and Statistics 5(1): (2016), 7–18

N. Kehayopulu and M. Tsingelis, Fuzzy sets in ordered groupoids, Semi-group Forum, 65 (2002), 128-132.

N. Kehayopulu, and M. Tsingelis, Regular ordered semigroups in terms of fuzzy subsets, Inform. Sci. 176 (2006), 3675-3693.

N. Kehayopulu, and M. Tsingelis, Fuzzy bi-ideals in ordered semigroups. Inf Sci 171(2005), 13–28.

A. Khan and M. Shabir, (α,β)-fuzzy interior ideals in ordered semigroups, Lobachevskii Journal of Mathematics, Volume 30, Number 1/January, (2009), 30-39.

A. Khan, Y. B. Jun and Z. Abbas, Characterizations of ordered semigroups by (∈,∈ ∨q)-fuzzy interior ideals, Neural Computing and Applications. DOI: 10.1007/s00521-010-0463-8

A. Khan, N. H. Sarmin, B. Davvaz and F. M. Khan, New types of fuzzy bi-ideals in ordered semigroups, Neural Comput & Applic (2012) 21 (Suppl 1):S295–S305

A. Khan, Y. B. Jun, N. H. Sarmin and F. M. Khan, Ordered semigroups characterized by (∈,∈ ∨q k )-fuzzy generalized bi-ideals, Neural Comput & Applic (2012) 21 (Suppl 1):S121–S132

F. M. Khan, N. H. Sarmin and A. Khan, Some study of (α,β)-fuzzy ideals in ordered semigroups, Annals of Fuzzy Mathematics and Informatics , 3 (2), (2012), 213- 227

A. Khan, N. H. Sarmin, F. M. Khan and Faizullah, Semiprime (∈,∈ ∨q k )-fuzzy quasi-ideals in ordered semigroups,World Applied Sciences Journal 16 (12): (2012), 1688-1698,

N. M. Khan, B. Davvaz and M. A. Khan, Ordered semigroups characterized in terms of generalized fuzzy ideals, Journal of Intelligent & Fuzzy Systems 32 (2017), 1045–1057.

A. Khan, M. M. Khalaf and M. Sakoor, More general forms of (∈,∈ ∨q k )-fuzzy filters of ordered semigroups, Honam Mathematical J. 2(39): (2017), 199–216.

X. Ma, J. Zhan and Y. B. Jun, On (∈,∈ ∨q)-fuzzy filters of R 0 -algebras, Math. Log. Quart. 55 (2009), 493-508.

X. Ma, J. Zhan and Y. Xu, Generalized fuzzy filters of R 0 -algebras, Soft Computing 11 (2007), 1079-1087.

J. N. Mordeson, D. S. Malik and N. Kuroki, Fuzzy Semigroups, Studies in Fuzziness and Soft Computing Vol. 131, Springer-Verlag Berlin (2003).

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.

A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl. 35 (1971), 512-517.

M. Shabir, Y. B. Jun and Y. Nawaz, Characterizations of regular semigroups by (α,β)-fuzzy ideals, Comput. Math. Appli. 59 (2010), 161-175.

M. Shabir, Y. B. Jun and Y. Nawaz, Semigroups characterized by (∈,∈ ∨q k )-fuzzy ideals, Comput. Math. Appl. 60 (2010), 1473-1493.

M. Shabir and A. Khan, Characterizations of ordered semigroups by the properties of their fuzzy generalized bi-ideals, New Mathematics and Natural Computation, 4 (2) (2008), 237-250.

L. A. Zadeh, Fuzzy Sets, Inform. & Control 8 (1965), 338 -353.



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