Affiliations: [a] Department of Mathematics, University of Tabuk, Tabuk, Saudi Arabia
| [b] Department of Mathematics, Madanapalle Institute of Technology & Science, Madanapalle, India
| [c] Department of Mathematics, Aligarh Muslim University, Aligarh, India
| [d] Department of Mathematics and Statistic, College of Science, Taif University, Taif, Saudi Arabia
Correspondence:
[*]
Corresponding author. G. Muhiuddin, Department of Mathematics, University of Tabuk, Tabuk 71491, Saudi Arabia. E-mail: [email protected].
Note: [1] Department of Mathematics and Statistic, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi Arabia. E-mail: [email protected].
Abstract: 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.
