The concept of interval-valued (${alpha},{eta}$)-fuzzy ideals, interval-valued (${alpha},{eta}$)-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. Regular LA-semigroups are characterized by the properties of the lower part of interval-valued (${in},{in}{vee}q$)-fuzzy left ideals, interval-valued (${in},{in}{vee}q$)-fuzzy quasi-ideals and interval-valued (${in},{in}{vee}q$)-fuzzy generalized bi-ideals. Main Facts.