In this paper, we introduce new types of fuzzy (m, n)-ideals in ordered semigroups. In fact, the notion of (∈ , ∈ ∨ (κ*, qκ))-fuzzy (m, n)-ideals of the ordered semigroups is introduced. Further, we present the characterzations of this notion in different ways. Then the (κ*, κ)-lower part of the (∈ , ∈ ∨ (κ*, qκ))-fuzzy (m, n)-ideals is defined and its associated properties are investigated. After that, (m, n)-regular ordered semigroups are characterized in terms of its (∈ , ∈ ∨ (κ*, qκ))-fuzzy (m, n)-ideals and their (κ*, κ)-lower parts.
BussabanL. and ChangphasT., On (m, n)-ideals on (m, n)-regular ordered semigroups, Songklanakarin J Sci Tech38(2) (2016), 199–206.
2.
JunY.B., KhanA. and ShabirM., Ordered semigroup characterized by their (∈, ∈ ∨)-fuzzy bi-ideals, Bull Malays Math Soc32(3) (2009), 391–408.
3.
JunY.B., OzturkM.A. and MuhiuddinG., A novel generalization of fuzzy subsemigroups, Annals of Fuzzy Mathematics and Informatics14(4) (2017), 359–370.
4.
JunY.B., SongS.Z. and MuhiuddinG., Hesitant fuzzy semigroups with a frontier, Journal of Intelligent and Fuzzy Systems30(3) (2016), 1613–1618.
5.
JunY.B., SongS.Z. and MuhiuddinG., Concave Soft Sets, Critical Soft Points, and Union-Soft Ideals of Ordered Semigroups, The ScientificWorld Journal2014 Article ID 467968, (2014), 11.
6.
KehayopuluN. and TsingelisM., Fuzzy sets in ordered groupoids, Semigroup Forum65 (2002), 128–132.
7.
KhanN.M., DavvazB. and KhanM.A., Ordered semigroups characterized in terms of generalized fuzzy ideals, Journal of Intelligent and Fuzzy Systems32(1) (2017), 1045–1057.
8.
KhanA., JunY.B., SarminN.H. and KhanF.M., Ordered semigroups characterized by (∈, ∈ ∨ qκ)-fuzzy generalized biideals, Neural Comput and Applic21(suppl.) (2012), 121–132.
9.
KhanM.A. and KhanN.M., Fuzzy fiters of ordered semigroups, Annals of Fuzzy Mathematics and Informatics12(6) (2016), 835–853.
10.
KurokiN., Fuzzy bi-ideals in semigroups, Comment Math Univ St Pauli28 (1979), 17–21.
11.
MahboobA., SalamA., AliM.F. and KhanN.M., Characterizations of Regular Ordered Semigroups by (∈, ∈ ∨ (κ*, qκ))-Fuzzy Quasi-Ideals, Mathematics7 (2019), 401.
12.
MuhiuddinG., MahboobA. and KhanN.M., A new type of fuzzy semiprime subsets in ordered semigroups, Journal of Intelligent and Fuzzy Systems37(3) (2019), 4195–4204.
13.
MuhiuddinG. and MahboobA., Int-soft ideals over the soft sets in ordered semigroups, AIMS Mathematics5(3) (2020), 2412–2423.
14.
MuhiuddinG., Cubic interior ideals in semigroups, Applications and Applied Mathematics14(1) (2019), 463–474.
15.
MuhiuddinG., RehmanN. and JunY.B., A generalization of (∈, ∈ ∨ q)–fuzzy ideals in ternary semigroups, Annals of Communications in Mathematics2(2) (2019), 73–83.
16.
MuhiuddinG., AlanaziA.M., MahboobA. and Al-KadiD., Generalized hesitant fuzzy ideals in semigroups, Journal of Mathematics2020 Article ID 8856287, (2020), 12.
17.
MuhiuddinG., Neutrosophic Subsemigroups, Annals of Communications in Mathematics1(1) (2018), 1–10.
18.
RosenfeldA., Fuzzy subgroups, J Math Anal Appl35 (1971), 512–517.
19.
ShabirM., JunY.B. and NawazY., Characterizations of regular semigroups by (∈, ∈ ∨ qκ)-fuzzy ideals, Comput Math Appl59 (2010), 539–549.
20.
ZadehL.A., Fuzzy sets, Information and Control8(1965), 338–353.
