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

Research paper by Muhammad Aslam, Saleem Abdullah, Samreen Aslam

Indexed on: 11 Jan '13Published on: 11 Jan '13Published in: Afrika Matematika

#### 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.