Abstract
The concept of interval-valued ((alpha) over bar, (beta) over bar)-fuzzy ideals, interval-valued ((alpha) over bar, (beta) over bar)-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 ((is an element of) over bar, (is an element of) over bar V (q) over bar)-fuzzy left ideals, interval-valued ((is an element of) over bar, (is an element of) over bar V (q) over bar)-fuzzy quasi-ideals and interval-valued ((is an element of) over bar, (is an element of) over bar V (q) over bar)-fuzzy generalized bi-ideals.