Ordered semigroups characterized in terms of generalized fuzzy ideals

Article type: Research Article

Authors: Khan, Noor Mohammad^a | Davvaz, Bijan^b | Khan, Mohammad Aasim^{a; *}

Affiliations: [a] Department of Mathematics, Aligarh Muslim University, Aligarh, India | [b] Department of Mathematics, Yazd University, Yazd, Iran

Correspondence: [*] Corresponding author. Mohammad Aasim Khan, Department of Mathematics, Aligarh Muslim University, Aligarh, India. Tel.: +919795905162; E-mail: [email protected].

Abstract: In the present paper, the notions of (k*, q)-quasi-coincident, (∈ , ∈ ∨ (k*, qk))-fuzzy left ideal, (∈ , ∈ ∨ (k*, qk))-fuzzy right ideal and (∈ , ∈ ∨ (k*, qk))-fuzzy generalized bi-ideal of an ordered semigroup are introduced. The (k*, k)-lower parts of an (∈ , ∈ ∨ (k*, qk))-fuzzy left ideal, (∈ , ∈ ∨ (k*, qk))-fuzzy right ideal and (∈ , ∈ ∨ (k*, qk))-fuzzy generalized bi-ideal are also defined. Then, we characterize these various fuzzy ideals. Finally, using the properties of these fuzzy ideals, we characterize regular, left regular, right regular, completely regular and left weakly regular ordered semigroups.

Keywords: Fuzzy ideals, (∈ , ∈ ∨ (k^*, q_k))-fuzzy ideals, regular, completely regular and left weakly regular ordered semigroups

DOI: 10.3233/JIFS-16339

Journal: Journal of Intelligent & Fuzzy Systems, vol. 32, no. 1, pp. 1045-1057, 2017