The main goal of this paper is to study ordered semihypergroups in the framework of uni-soft left (right) hyperideals. The notions of uni-soft semihypergroups, uni-soft left (right) hyperideals are introduced, and the related properties are investigated. The concept of exclusive set is provided and the characterizations of ordered semihypergroups in terms of uni-soft left (right) hyperideals are studied. The notions of uni-soft product is considered and their properties related to uni-soft left (right) hyperideals are studied. Using the notions of uni-soft left (right) hyperideals, the main theorems for a regular and intra-regular ordered semihypergroups are investigated. The concepts of a concave soft set and critical soft point in ordered semihypergroups are provided and the basic properties of these notions are given.
AcarU., KoyuncuF. and TanayB., Soft sets and soft rings, Computers & Mathematics with Applications59 (2010), 3458–3463.
2.
AtagunA.O. and SezginA., Soft substructures of rings, fields and modules, Computers & Mathematics with Applications61 (2011), 592–601.
3.
AzharM., YaqoobN., GulistanM. and KhalafM.M., On (∈, ∈∨qk)-Fuzzy hyperideals in ordered LAsemihypergroups, Discrete Dynamics in Nature and Society, 2018 (2018), Article ID 9494072, 13 pages.
4.
CagmanN. and EnginogluS., FP-soft set theory and its applications, Annals of Fuzzy Mathematics and Informatics2 (2011), 219–226.
5.
CorsiniP.Prolegomena of Hypergroup Theory, Aviani Editore, Italy, 1993.
6.
FengF., Soft rough sets applied to multicriteria group decision making, Annals of Fuzzy Mathematics and Informatics2 (2011), 69–80.
7.
FengF., JunY.B. and ZhaoX., Soft irings, Computers & Mathematics with Applications56 (2008), 2621–2628.
8.
GulistanM., YaqoobN., VougiouklisT. and WahabH.A., Extensions of cubic ideals in weak left almost semihypergroups, Journal of Intelligent & Fuzzy Systems34 (2018), 4161–4172.
9.
HilaK. and AbdullahS., A study on intuitionistic fuzzy sets in γ-semihypergroups, Journal of Intelligent & Fuzzy Systems26 (2014), 1695–1710.
10.
HilaK., DavvazB. and NakaK., On quasi-hyperideals in semihypergroups, Communications in Algebra39 (2011), 4183–4194.
11.
HeidariD. and DavvazB., On ordered hyperstructures, U.P.B. Sci Bull Series A73(2) (2011), 85–96.
12.
JunY.B., SongS.Z. and MuhiuddinG., Concave Soft Sets, Critical soft points, and union-soft Ideals of ordered semigroups, The Scientific World Journal2014 (2014), Article ID 467968, 11 pages.
13.
JunY.B., Soft BCK/BCI-algebras, Computers & Mathematics with Applications56 (2008), 1408–1413.
14.
JunY.B. and AhnS.S., Double-framed soft sets with applications in BCK/BCI-algebras, Journal of Applied Mathematics2012 (2012), Article ID 178159, 15 pages.
JunY.B., LeeK.J. and ParkC.H., Soft set theory applied to ideals in d-algebras, Computers & Mathematics with Applications57 (2009), 367–378.
17.
JunY.B., LeeK.J. and ZhanJ., Soft p-ideals of soft BCI-algebras, Computers & Mathematics with Applications58 (2009), 2060–2068.
18.
JunY.B. and ParkC.H., Applications of soft sets in ideal theory of BCK/BCI-algebras, Information Sciences178 (2008), 2466–2475.
19.
KhanA., KhanR., JunB.Y. and ShahS.I.A., Applications of soft union sets to ordered semigroups via uni-soft quasi-ideals, Journal of Intelligent & Fuzzy Systems30 (2016), 97–107.
20.
KhanA., TangJ. and LuoY., Characterizations of semisimple ordered ihypergroups in terms of fuzzy hyperideals, Journal of Intelligent & Fuzzy Systems30 (2016), 1735–1753.
21.
KhanA., JunY.B. and KhanR., Uni-soft structure applied to ordered semigroups, Soft Computing21 (2017), 1021–1030.
22.
MolodtsovD., Soft set theory - First results, Computers & Mathematics with Applications37 (1999), 19–31.
23.
MajiP.K., BiswasR. and RoyA.R., Soft set theory, Computers & Mathematics with Applications45 (2003), 555–562.
24.
MajiP.K., RoyA.R. and BiswasR., An application of soft sets in a decision making problem, Computers & Mathematics with Applications44 (2002), 1077–1083.
25.
MartyF., Sur une generalization de la notion de group, in: Proc 8th Congress Mathematics Scandenaves, Stockholm, 1934, 45–49.
26.
NazS. and ShabirM., On prime soft bi-hyperideals of semihypergroups, Journal of Intelligent & Fuzzy Systems26 (2014), 1539–1546.
27.
PibaljommeeB. and DavvazB., Some study of several kinds of fuzzy hyperideals in ordered semihypergroups, International Congress on Algebraic Hyperstructures and its Applications, Xanthi, Greece, 2014, 91–94.
28.
PibaljommeeB. and DavvazB., Characterizations of (fuzzy) bi-hyperideals in ordered semihypergroups, Journal of Intelligent & Fuzzy Systems28 (2015), 2141–2148.
29.
YaqoobN., AslamM., DavvazB. and GhareebA., Structures of bipolar fuzzy & γ-hyperideals in γ-semihypergroups, Journal of Intelligent & Fuzzy Systems27 (2014), 3015–3032.
30.
YaqoobN., AkramM. and AslamM., Intuitionistic fuzzy soft groups induced by (t; s)-norm, Indian Journal of Science and Technology6 (2013), 4282–4289.
