Abstract
The concept of interval-valued \((\overline{\alpha },\overline{\beta })\)-fuzzy ideals, interval-valued \((\overline{\alpha },\overline{\beta })\)-fuzzy generalized bi-ideals are introduced in LA-semigroups, using the ideas of belonging and quasi-coincidence of an interval-valued fuzzy point with an interval-valued fuzzy set and some related properties are investigated. We define the lower and upper parts of interval-valued fuzzy subsets of an LA-semigroup. Also regular LA-semigroups are characterized by the properties of the upper part of interval-valued \((\overline{\in }, \overline{\in }\vee \overline{q})\)-fuzzy left ideals, interval-valued \(( \overline{\in },\overline{\in }\vee \overline{q})\)-fuzzy quasi-ideals and interval-valued \((\overline{\in },\overline{\in }\vee \overline{q})\)-fuzzy generalized bi-ideals.
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Aslam, M., Abdullah, S. & Aslam, S. Characterization of regular LA-semigroups by interval-valued \((\overline{\alpha },\overline{\beta })\)-fuzzy ideals. Afr. Mat. 25, 501–518 (2014). https://doi.org/10.1007/s13370-012-0130-6
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DOI: https://doi.org/10.1007/s13370-012-0130-6
Keywords
- Interval-valued \((\overline{\alpha }, \overline{\beta })\)-fuzzy sub LA-semigroups
- Interval-valued \((\overline{\alpha }, \overline{\beta })\)-fuzzy ideals
- Interval-valued \((\overline{\alpha }, \overline{\beta })\)-fuzzy
- Interval-valued \((\overline{\alpha }, \overline{\beta })\)-fuzzy quasi-ideals