, Volume 25, Issue 3, pp 501-518
Date: 11 Jan 2013

Characterization of regular LA-semigroups by interval-valued \((\overline{\alpha },\overline{\beta })\) -fuzzy ideals

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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.