Ordered semigroups characterized by their intuitionistic fuzzy bi-ideals

Document Type: Research Paper

Authors

1 Department of Mathematics, COMSATS Institute of IT Abbottabad, Pakistan

2 Department of Mathematics Educations and RINS , Gyengsang National University , Chinju 660-701, Korea

3 Department of Mathematics Quaid-i-Azam University, Islamabad, Pakistan

Abstract

Fuzzy bi-ideals play an important role in the study of ordered semigroup
structures. The purpose of this paper is to initiate and study the
intiuitionistic fuzzy bi-ideals in ordered semigroups and investigate the
basic theorem of intuitionistic fuzzy bi-ideals. To provide the
characterizations of regular ordered semigroups in terms of intuitionistic
fuzzy bi-ideals and to discuss the relationships of left(resp. right and
completely regular) ordered semigroups in terms intuitionistic fuzzy
bi-ideals.

Keywords


bibitem{1} K. T. Atanassov, textit{Intuitionistic fuzzy sets}, Fuzzy Sets
and Systems, textbf{20} (1986), 87-96.

bibitem{2} K. T. Atanassov, textit{New operations defined over the
intuitionistic fuzzy sets}, Fuzzy Sets and Systems, $mathbf{61}$ $ (1994)$, $%
137 $-$142$.

bibitem{3} K. T. Atanassov, textit{Intuitionistic fuzzy sets, theory and
applications}, Studies in Fuzziness and Soft Computing, Heidelberg,
Physica-Verlag, $mathbf{35}$ $ (1999)$.

bibitem{4} R. A. Borzooei and Y. B. Jun, textit{Intuitionistic fuzzy hyper
BCK-ideals of hyper BCK-algebras, }Iranian Journal of Fuzzy Systems, textbf{%
1}textbf{(1)} (2006), 23-29.

bibitem{5} P. Burillo and H. Bustince, textit{Vague sets are
intuitionistic fuzzy sets}, Fuzzy Sets and Systems textbf{79} (1996),
403-405.

bibitem{6} B. Davvaz, W. A. Dudek and Y. B. Juntextit{, Intuitionistic fuzzy }$%
H_{v}$textit{-submodules}, Information Sciences, $mathbf{176}$ $(2006)$, $%
285 $-$300$.

bibitem{7} S. K. De, R. Biswas and A. R. Roy, textit{An application of
intuitionistic fuzzy sets in medical diagnosis}, Fuzzy Sets and Systems,
textbf{117} (2001), 209-213.

bibitem{8} L. Dengfeng and C. Chunfian, textit{New similarity measures of
intuitionistic fuzzy sets and applications to pattern recognitions}, Pattern
Reconit. Lett., textbf{23} (2002), 221-225.

bibitem{9} W. L. Gau and D. J. Buehre, textit{Vague sets}, IEEE Trans Syst
Man Cybern, textbf{23} (1993), 610-614.

bibitem{10} S. B. Hosseini, D. Oregan and R. Saadati, textit{Some results on
intuitionistic fuzzy spaces}, Iranian Journal of Fuzzy Systems, textbf{4}textbf{(1)} (2007), 53-64.

bibitem{11} K. Hur, S. Y. Jang and H. W. Kang, textit{Some intuitionistic
fuzzy congruences}, Iranian Journal of Fuzzy Systems, textbf{3}textbf{(1)} (2006),
45-57.

bibitem{12} Y. B. Jun, textit{Intuitionistic fuzzy bi-ideals of ordered
semigroups}, KYUNGPOOK Math. J., $mathbf{45}$ $(2005)$, $527$-$537$.

bibitem{13} N. Kehayopulu, textit{On regular duo ordered semigroups},
Math. Japonica, $mathbf{37}$$textbf{(6)}$ $(1990)$, $1051$-$1056$.

bibitem{14} N. Kehayopulu and M. Tsingelis, textit{Fuzzy sets in ordered
groupoids}, Semigroup Forum $mathbf{65}$ $(2002)$, $128$-$132$.

bibitem{15} N. Kehayopulu and M. Tsingelis, textit{Fuzzy bi-ideals in
ordered semigroups}, Information Sciences, $mathbf{171}$ $(2005)$, $13$-$28$.

bibitem{16} N. Kehayopulu and M. Tsingelis, textit{Regular ordered
semigroups in terms of fuzzy subset}, Information Sciences, $mathbf{176}$ $%
(2006)$, $65$-$71$.

bibitem{17} N. Kehayopulu and M. Tsingelis, textit{Left and intra-regular
ordered semigroups in terms fuzzy sets}, Quasigroups and Related Systems,
textbf{14} (2006), 169-178.

bibitem{18} N. Kehayopulu and M. Tsingelis, textit{Fuzzy ideals in ordered
semigroups}, Quasigroups and Related Systems, textbf{15} (2007), 279-289.

bibitem{19} K. H. Kim and Y. B. Jun, textit{Intuitionistic fuzzy interior
ideals of semigroups,} Int. J. Math. Math. Sci., $mathbf{{27}(5)}$ $ (2001)$, $%
261 $-$267.$

bibitem{20} K. H. Kim and Y. B. Jun, textit{Intuitionistic fuzzy ideals of
semigroups}, Indian J. Pure Appl. Math., $mathbf{{33}(4)}$ $(2002)$, $443$-$449$.

bibitem{21} K. H. Kim, W. A. Dudek and Y. B. Jun, textit{Intuitionistic
fuzzy subquasigroups of quasigroups}, Quasigroups Related Systems, textbf{7} (2000), 15-28.

bibitem{22} M. Rafi and M. S. M. Noorani, textit{Fixed point theorem on
intuitionistic fuzzy metric spaces}, Iranian Journal of Fuzzy Systems,
textbf{{3}(1)} (2006), 23-29.

bibitem{23} M. Shabir and A. Khan, textit{Characterizations of ordered
semigroups by the properties of their fuzzy generalized bi-ideals}, New
Math. Natural Comput., $mathbf{{4}(2)}$ ($2008$), $237$-$250$.

bibitem{24} M. Shabir and A. Khan, textit{Intuitionistic fuzzy interior
ideals of ordered semigroups}, to appear in J. Applied Math. and
Informatics.

bibitem{25} M. Shabir and A. Khan, textit{Ordered semigroups characterized
by their intuitionistic fuzzy generalized bi-ideals}, to appear in Fuzzy
Systems and Mathematics.

bibitem{26} E. Szmidt and J. Kacprzyk, textit{Entropy for intuitionistic
fuzzy sets}, Fuzzy Sets and Systems, textbf{118} (2001), 467-477.

bibitem{27} L. A. Zadeh, textit{Fuzzy sets}, Information  and  Control, $mathbf{8}$ $(1965)$, $338$-$353$.