It is known that any ordered semigroup embeds into the structure consisting of the set of all fuzzy sets together with an associative binary operation and a partial order with compatibility. In this study, we provide two classes of ordered semigroups in which any model in these classes is a representation of any ordered semigroup. Moreover, we give an interconnection of a class we constructed.
AdemA., ÇakıtE. and DagdevirenM., A fuzzy decision- makingapproach to analyze the design principles for green ergonomics, Neural Computing and Applications34 (2022), 1373–1384.
2.
Ali KhanM.S., AbdullahS., AliA., AminF. and RahmanK., Ongeneralized (∈, ∈ ∨ qk)-fuzzy quasi-ideals in orderedsemigroups, Turkish Journal of Fuzzy Systems8 (2017), 33–51.
3.
Al-TahanM., DavvazB., MahboobA., Hoskova-MayerovaS. and VagaskáA., On New Filters in Ordered Semigroups, Symmetry14 (2022), 1564.
4.
BirkhoffG., Lattice theory, American Mathematical Society (1967).
5.
BoltürkE., Fuzzy sets theory and applications in engineeringeconomy, Journal of Intelligent & Fuzzy Systems42(2022), 37–46.
6.
ChenH., DasS., MorganJ.M. and MaharatnaK., Prediction andclassification of ventricular arrhythmia based on phase-spacereconstruction and fuzzy c-means clustering, Computers in Biology and Medicine142 (2022), 105180.
7.
DavvazB. and KhanA., Characterizations of regular ordered semigroups in terms of (α, β)-fuzzy generalizedbi-ideals, Information Sciences181 (2011), 1759–1770.
8.
FengY. and CorsiniP., (λ, μ)-fuzzy ideals of ordered semigroups, Annals of Fuzzy Mathematics and Informatics4 (2012), 123–129.
9.
JunY.B., KhanA. and ShabirM., Ordered semigroups characterized bytheir (∈, ∈ ∨ q)-fuzzy bi-ideals, Bulletin of the Malaysian Mathematical Sciences Society32 (2009), 391–408.
10.
JunY.B., TinpunK. and LekkoksungN., Characterizing some regularities of ordered semigroups by generalized fuzzy ideals, (submitted).
11.
KhanN.M., DavvazB. and KhanM.A., Ordered semigroups characterizedin terms of generalized fuzzy ideals, Journal of Intelligent & Fuzzy Systems32 (2017), 1045–1057.
12.
KhanA., JunY.B. and AbbasM.Z., Characterizations of orderedsemigroups in terms of (∈, ∈ ∨ qk)-fuzzy interiorideals, Neural Computing and Applications21 (2012), 433–440.
13.
KhanA., JunY.B., SarminN.H. and KhanF., Ordered semigroupscharacterized by (∈, ∈ ∨ qk)-fuzzy generalizedbi-ideals, Neural Computing and Applications21 (2012), 121–132.
14.
KhanA., SarminN.H., DavvazB. and KhanF.M., New types of fuzzybi-ideals in ordered semigroups, Neural Computing andApplications21 (2012), 295–305.
15.
KhanF.M., SarminN.H. and KhanA., Some new characterization ofordered semigroups in terms of (λ, θ)-fuzzybi-ideals, International Journal of Algebra and Statistics1 (2012), 22–32.
16.
KhanF.M., SarminN.H. and KhanA., Some study of (α,β)- fuzzy ideals in ordered semigroups, Annals of FuzzyMathematics and Informatics3 (2012), 213–227.
17.
KehayopuluN. and TsingelisM., Fuzzy sets in ordered groupoids, Semigroup Forum65 (2002), 128–132.
18.
KehayopuluN. and TsingelisM., The embedding of an ordered groupoidinto a poe-groupoid in terms of fuzzy sets, Information Sciences152 (2003), 231–236.
19.
KehayopuluN. and TsingelisM., Fuzzy bi-ideals in orderedsemigroups, Information Sciences171 (2005), 13–28.
20.
KehayopuluN. and TsingelisM., Fuzzy interior ideals in ordered semigroups, Lobachevskii Journal of Mathematics21(2006), 65–71.
21.
KehayopuluN. and TsingelisM., Left regular and intra-regular ordered semigroups in terms of fuzzy subsets, Quasigroups and Related Systems14 (2006), 169–178.
22.
KehayopuluN. and TsingelisM., Regular ordered semigroups in termsof fuzzy subsets, Information Sciences176 (2006), 3675–3693.
23.
KehayopuluN. and TsingelisM., Fuzzy ideals in ordered semigroups, Quasigroups and Related Systems15 (2007), 279–289.
24.
KehayopuluN. and TsingelisM., Intra-regular ordered semigroups interms of fuzzy sets, Lobachevskii Journal of Mathematics30 (2009), 23–29.
25.
KurokiN., Fuzzy bi-ideals in semigroups, CommentariiMathematici Universitatis Sancti Pauli28 (1980), 17–21.
26.
ManzoorR., KhanA., YousafzaiF. and AmjadV., Fuzzy quasiidealswith thresholds (α, β] in ordered semigroups, International Journal of Algebra and Statistics2 (2013), 72–82.
27.
MuhiuddinG., MahboobA., KhanN.M. and Al-KadiD., New types offuzzy (m, n)-ideals in ordered semigroups, Journal of Intelligent & Fuzzy Systems41 (2021), 6561–6574.
28.
RosenfeldA., Fuzzy groups, Journal of Mathematical Analysisand Applications35 (1971), 512–517.
29.
ShenY., Calculus for linearly correlated fuzzy number-valuedfunctions, Fuzzy Sets and Systems429 (2022), 101–135.
30.
TirunehG.G., FayekA.R. and SumatiV., Neuro-fuzzy systems inconstruction engineering and management research, Automation119 (2020), 103348.
31.
XieX.Y. and TangJ., Regular ordered semigroups and intraregular ordered semigroups in terms of fuzzy subsets, Iranian Journal of Fuzzy Systems7 (2010), 121–140.
32.
XieX.Y. and YanF., Fuzzy ideals extenstions of ordered semigroups, Lobachevskii Journal of Mathematics19 (2005), 29–40.
33.
ZadehL.A., Fuzzy sets, Information and Control8(1965), 338–353.
34.
ZhaoM., HanY. and ZhouJ., An extensive operational law formonotone functions of LR fuzzy intervals with applications to fuzzy optimization, Soft Computing26 (2022), 11381–11401.
35.
ZhuB., YangT. and YanZ., Finite time annular domain robuststability analysis and controller design for TS fuzzy intervalpositive systems, IEEE Access10 (2022), 24255–24263.
