More General Forms of $(alpha, beta )$-fuzzy Ideals of Ordered Semigroups

Yin, Yunqiang; Jun, Young Bae; Yang, Zhihui

doi:10.22111/ijfs.2012.135

Document Type : Research Paper

Authors

¹ State Key Laboratory, Breeding Base of Nuclear Resources and Environment, East China Institute of Technology, Nanchang, 330013, China

² Department of Mathematics Education (and RINS), Gyeongsang Na- tional University, Chinju 660-701, Korea

³ School of Mathematics and Information Sciences, East China Institute of Technology, Fuzhou, Jiangxi 344000, China

https://doi.org/10.22111/ijfs.2012.135

Abstract

This paper consider the general forms of $(alpha,beta)$-fuzzy
left ideals (right ideals, bi-ideals, interior ideals) of an ordered
semigroup, where
$alpha,betain{in_{gamma},q_{delta},in_{gamma}wedge
q_{delta}, in_{gamma}vee q_{delta}}$ and $alphaneq
in_{gamma}wedge q_{delta}$. Special attention is paid to
$(in_{gamma},ivq)$-left ideals (right ideals, bi-ideals, interior
ideals) and some related properties are investigated. The
characterization of regular ordered semigroups in terms of
$(in_{gamma},ivq)$-fuzzy left (right) ideals,
$(in_{gamma},ivq)$-fuzzy bi-ideals and
$(in_{gamma},ivq)$-fuzzy interior ideals is also investigated.

Keywords

References

bibitem{Bhakat1992} S. K. Bhakat and P. Das, {it On the definition of a fuzzy
subgroup}, Fuzzy Sets and Systems, textbf{51} (1992), 235-241.

bibitem{Bhakat1996} S. K. Bhakat and P. Das, {it $(in,invee q)$-fuzzy
subgroups}, Fuzzy Sets and Systems, textbf{80} (1996), 359-368.

bibitem{Bhakat2000} S. K. Bhakat, {it$(in,invee q)$-fuzzy normal,
quasinormal and maximal subgroups}, Fuzzy Sets and Systems, textbf{112}
(2000), 299-312.

bibitem{Bhakat1999} S. K. Bhakat, {it $(in,invee q)$-level subsets},
Fuzzy Sets and Systems, textbf{103} (1999), 529-533.

bibitem{Kehayopulu} N. Kehayopulu and M. Tsingelis, {it Fuzzy sets in
ordered groupoids}, Semigroup Forum, textbf{65} (2002), 128-132.

bibitem{Kehayopulu1} N. Kehayopulu and M. Tsingelis, {it Fuzzy interior ideals in ordered
semigroups}, Lobachevskii J. Math., textbf{21} (2006), 65-71.

bibitem{Kehayopulu2} N. Kehayopulu and M. Tsingelis, {it Fuzzy bi-ideals in orderd semigroups},
Information Sciences, textbf{171} (2005), 13-28.

bibitem{Kehayopulu3} N. Kehayopulu and M. Tsingelis, {it Regular ordered semigroups in terms of
fuzzy subset}, Information Sciences, textbf{176} (2006), 3675-3693.

bibitem{Kehayopulu4} N. Kehayopulu and M. Tsingelis, {it Characterization of some types of ordered semigroups in terms of
fuzzy sets}, Lobachevskii J. Math., textbf{29} (2008), 14-20.

bibitem{2} A. Khan, Y. B. Jun and M. Shabir, {it Ordered semigroups characterized
by their intuitionistic fuzzy bi-ideals}, Iranian Journal of Fuzzy
Systems, textbf{7} (2010 ), 55-69.

bibitem{Khan} A. Khan and M. Shabir, {it $(alpha,beta)$-fuzzy interior ideals in ordered
semigroups}, Lobachevskii J. Math., textbf{30} (2009), 30-39.

bibitem{Pu1980} P. M. Pu and Y. M. Liu, {it Fuzzy topology I: neighbourhood structure of a
fuzzy point and Moore¨CSmith convergence}, J. Math. Anal. Appl.,
textbf{76} (1980), 571-599.

bibitem{Rosenfeld} A. Rosenfeld, {it Fuzzy groups}, J. Math. Anal. Appl, textbf{35} (1971), 512-517.

bibitem{1} M. Shabir, Y. B. Jun and M. Bano, {it On prime fuzzy bi-ideals of
semigroups}, Iranian Journal of Fuzzy
Systems, textbf{7} (2010 ), 115-128.

bibitem{Shabir} M. Shabir and A. Khan, {it Characterizations of ordered semigroups by the properties of generalized fuzzy bi-ideals}, New Math. Nat. Comput., textbf{4(2)}
(2008), 237-250.

bibitem{Shabir1} M. Shabir and A. Khan, {it Characterizations of ordered semigroups by the properties of their
fuzzy ideals}, Comput. Math. Appl., textbf{59} (2010), 539-549.

bibitem{3} X. Y. Xie and J. Tang, {it Regular ordered semigroups and intra-regular ordered semigroups
in terms of fuzzy subsets}, Iranian Journal of Fuzzy
Systems, textbf{7} (2010),
121-140.

bibitem{Yin} Y. Yin and H. Li, {it The characterization of regular and intra-regular ordered semigroups}, Ital. J. Pure Appl. Math.,
textbf{24} (2008), 41-52.

bibitem{Zadeh1965} L. A. Zadeh, {it Fuzzy sets}, Information and Control, textbf{8} (1965), 338-358.

More General Forms of $(alpha, beta )$-fuzzy Ideals of Ordered Semigroups

References

References

Volume 9, Issue 4 - Serial Number 4September and October 2012Pages 99-113

Volume 9, Issue 4 - Serial Number 4
September and October 2012
Pages 99-113