Abstract: We introduce the concept of quansi-coincidence of a fuzzy interval value with an interval valued fuzzy set, propose the notions of interval valued fuzzy LA-subsemigroup and interval valued fuzzy left(right, bi-, interior)ideals of LA-semigroups, generalize them to interval valued(∈,∈∨q)-fuzzy LA-subsemigroup and interval valued(∈,∈∨q)-fuzzy left(right, bi-, interior)ideals, respectively, and study their related properties and equivalent characterizations. In particular, the concept of a fuzzy subgroup with thresholds is generalized to the concept of interval valued fuzzy LA-subsemigroup and interval valued fuzzy left(right, bi-, interior)ideals in LA-semigroups.