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(∈, ∈ ∨qk)-FUZZY IDEALS IN LEFT REGULAR ORDERED -SEMIGROUPS
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  • Journal title : Honam Mathematical Journal
  • Volume 35, Issue 4,  2013, pp.583-606
  • Publisher : The Honam Mathematical Society
  • DOI : 10.5831/HMJ.2013.35.4.583
 Title & Authors
(∈, ∈ ∨qk)-FUZZY IDEALS IN LEFT REGULAR ORDERED -SEMIGROUPS
Yousafzai, Faisal; Khan, Asghar; Khan, Waqar; Aziz, Tariq;
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 Abstract
We generalize the idea of (, )-fuzzy ordered semi-group and give the concept of (, )-fuzzy ordered -semigroup. We show that (, )-fuzzy left (right, two-sided) ideals, (, )-fuzzy (generalized) bi-ideals, (, )-fuzzy interior ideals and (, )-fuzzy (1, 2)-ideals need not to be coincide in an ordered -semigroup but on the other hand, we prove that all these (, )-fuzzy ideals coincide in a left regular class of an ordered -semigroup. Further we investigate some useful conditions for an ordered -semigroup to become a left regular ordered -semigroup and characterize a left regular ordered -semigroup in terms of (, )-fuzzy one-sided ideals. Finally we connect an ideal theory with an (, )-fuzzy ideal theory by using the notions of duo and ()-fuzzy duo.
 Keywords
ordered -semigroups;fuzzy point;(, )-fuzzy ideals;
 Language
English
 Cited by
1.
Existence of non-associative algebraic hyper-structures and related problems, Afrika Matematika, 2015, 26, 5-6, 981  crossref(new windwow)
 References
1.
Faisal, N. Yaqoob and A. Ghareeb, Left regular AG-groupoids in terms of fuzzy interior ideals, Afrika Mathematika, DOI: 10.1007/s13370-012-0081-y. crossref(new window)

2.
S.K. Bhakat and P. Das, On the denition of a fuzzy subgroup, Fuzzy Sets and Systems, 51 (1992), 235-241. crossref(new window)

3.
S.K. Bhakat and P. Das, (${\in},\;{\in}\;{\vee}q$)-fuzzy subgroups, Fuzzy Sets and Systems, 80 (1996), 359-368. crossref(new window)

4.
B. Davvaz, Fuzzy R-subgroups with threshholds of near-rings and implication operators, Soft Comput., 12 (2008), 875-879. crossref(new window)

5.
Y.B. Jun, Generalizations of (${\in},\;{\in}\;{\vee}q$)-fuzzy subalgebras in BCK/BCI-algebras, Comput. Math. Appl., 58 (2009), 1383-1390. crossref(new window)

6.
Y.B. Jun, A. Khan and M. Shabir, Ordered semigroups characterized by their (${\in},\;{\in}\;{\vee}q$)-fuzzy bi-ideals, Bull. Malaysian Math. Sci. Soc., 2(3) (2009), 391-408.

7.
Y.B. Jun and S.Z. Song, Generalized fuzzy interior ideals in semigroups, Inform. Sci., 176 (2006), 3079-3093. crossref(new window)

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.
V. Murali, Fuzzy points of equivalent fuzzy subsets, Inform. Sci., 158 (2004), 277-288. crossref(new window)

11.
Q. Mushtaq and S.M. Yusuf, On LA-semigroups, Aligarh. Bull. Math., 8 (1978), 65-70.

12.
Q. Mushtaq and S.M. Yusuf, On LA-semigroup dened by a commutative inverse semigroup, Math. Bech., 40 (1988), 59-62.

13.
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. crossref(new window)

14.
A. Rosenfeld, Fuzzy groups, J. Math. Anal. Appl., 35 (1971), 512-517. crossref(new window)

15.
M. Shabir, Y.B. Jun and Y. Nawaz, Semigroups characterized by (${\in},\;{\in}\;{\vee}qk$)-fuzzy bi-ideals, Computers and Mathematics with Applications, 60 (2010), 1473-1493. crossref(new window)

16.
N. Stevanovic and P.V. Protic, Composition of Abel-Grassmann's 3-bands, Novi Sad. J. Math., 2(34) (2004), 175-182.

17.
L. A. Zadeh, Fuzzy sets, Inform. Control., 8 (1965), 338-353. crossref(new window)