This paper addresses the strongly convex lattice-valued fuzzy (L-fuzzy) subsets of an ordered semigroup. It is shown that the set of all strongly convex L-fuzzy subsets of an ordered semigroup S forms a quantale and that S can be embedded into the quantale. The properties of L-fuzzy ideals of an ordered semigroup, a special class of strongly convex L-fuzzy subsets, are discussed. Specially, two approaches are developed to construct an L-fuzzy (left) ideal by an arbitrary L-fuzzy subset of an ordered semigroup.
BlythT.S., Lattices and ordered algebraic structures, Springer-Verlag, London, 2005.
4.
BorzooeiR.A., DvurecěnskijA. and
ZahiriO., L-ordered and L-lattice ordered groups, Information Sciences314 (2015), 118–134.
5.
DavvazB. and KhanA., Characterizations of regular ordered semigroups in terms of (α, β)-fuzzy generalized bi-ideals, Information Sciences181(2) (2011), 1759–1770.
6.
DavvazB. and KhanA., Generalized fuzzy filters in ordered semigroups, Iranian Journal of Science and TechnologyA1 (2012), 77–86.
7.
DavvazB., KhanA., SarminN.H. and KhanH., More general forms of interval valued fuzzy filters of ordered semigroups, Journal of Intelligent&Fuzzy Systems15(2) (2013), 110–126.
8.
DavvazB. and CorsiniP., Relationship between ordered semihypergroups and ordered semigroups by using pseudoorder, European Journal of Combinatorics44 (2015), 208–217.
9.
HanS.W. and ZhaoB., Q-fuzzy subsets on ordered semigroups, Fuzzy Sets and Systems210 (2013), 102–116.
10.
HöhleU., and ŠostakA.P.Axiomatic foundations of fixed-basis fuzzy topology, in:
HöhleU.,
RodabaughS.E. (Eds.), Mathematics of Fuzzy Sets-Logic, Toology, and Measure Theory, Kluwer Academic Publishers, Boston, Dordrecht, London, 1999, (Chapter 3).
11.
JunY.B., MengJ. and XinX.L., On ordered filters of implicative semigroups, Semigroup Forum54 (1997), 75–82.
12.
JunY.B., KhanA. and ShabirM., Ordered semigroups characterized by their (∈, ∈ ∨ q)-fuzzy bi-ideals, Bull Malays Math Sci Soc32(2) (2009), 391–408.
JunY.B., DavvazB. and KhanA., Filters of ordered semigroups based on the fuzzy points, Journal of Intelligent & Fuzzy Systems24(3) (2013), 619–630.
15.
KehayopuluN., On weakly prime ideals of ordered semigroups, Math Japon35(6) (1990), 1051–1056.
16.
KehayopuluN., XieX.Y. and TsingelisM., A characterization of prime and semiprime ideals of semigroups in terms of fuzzy subsets, Soochow J Math27(2) (2001), 139–144.
17.
KehayopuluN. and TsingelisM., The embedding of an ordered groupoid into a poe-groupoid in terms of fuzzy sets, Information Sciences152 (2003), 231–236.
18.
KehayopuluN. and TsingelisM., Fuzzy bi-ideals in ordered semigroups, Information Sciences171 (2004), 13–28.
19.
KehayopuluN. and TsingelisM., Regular ordered semigroups in terms of fuzzy subsets, Information Sciences176 (2006), 3675–3693.
20.
KhanA. and ShabirM., (α, β)-fuzzy interior ideals in ordered semigroups, Lobachevskii J Math29(1) (2009), 330–337.
21.
KhanA., JunY.B. and ShabirM., A study of generalized fuzzy ideals in ordered semigroups, Neural Comput Appl21(1) (2012), 69–78.
22.
KhanA., JunY.B., ShahS.I.A. and KhanR., Applications of soft union sets in ordered semigroups via uni-soft quasi-ideals, Journal of Intelligent & Fuzzy Systems30(1) (2015), 97–107.
23.
KhanH.U., SarminN.H., KhanA. and KhanF.M., Classification of ordered semigroups in terms of generalized intervalvalued fuzzy interior ideals, Journal of Intelligent Systems25(2) (2016), 297–318.
24.
PanX. and XuY., Lattice implication ordered semigroups, Information Sciences178(2) (2008), 403–413.
25.
ŠešeljaB.,
TepavčevićA. and UdovičićM., Fuzzy ordered structures and fuzzy lattice ordered groups, Journal of Intelligent & Fuzzy Systems27(3) (2014), 1119–1127.
26.
ShabirM. and KhanA., Characterizations of ordered semigroups by the properties of their fuzzy ideals, Comput Math Appl59(1) (2010), 539–549.
27.
ShabirM. and KhanA., On fuzzy ordered semigroups, Information Sciences274 (2014), 236–248.
28.
TangJ. and XieX.Y., Characterizations of regular ordered semigroups by generalized fuzzy ideals, Journal of Intelligent & Fuzzy Systems26(1) (2014), 239–252.
29.
XieX.Y., Ideals in lattice-ordered semigroups, Soochow Math J22 (1996), 75–84.
30.
XieX.Y., An introduction to ordered semigroup theory, Kexue Press, Beijing, 2001.
31.
XieX.Y. and TangJ., Fuzzy radicals and prime fuzzy ideals of ordered semigroups, Information Sciences178(22) (2008), 4357–4374.
32.
XieX.Y. and TangJ., Regular ordered semigroups and intraregular ordered igroups in terms of fuzzy subsets, Iran J Fuzzy Syst7 (2010), 121–140.
33.
YaoW., Quantitative domains via fuzzy sets: Part I: continuity of fuzzy directed-complete poset, Fuzzy Sets and Systems161 (2010), 983–987.
34.
YinY.Q. and ZhanJ.M., Generalized intuitionistic fuzzy ideals of ordered semigroups, Bull Malays Math Sci Soc34(3) (2011), 997–1015.
35.
YinY.Q. and ZhanJ.M., Characterization of ordered semigroups in terms of fuzzy soft ideals, Bull Malays Math Sci Soc35(4) (2012), 997–1015.
36.
ZhangQ.Y. and FanL., Continuity in quantitative domains, Fuzzy Sets and Systems154 (2005), 118–131.
