We introduce an extension of the Description Logic FL₀that allows us to define concepts in an approximate way. More precisely, we extend FL₀with a threshold concept constructor of the form C_▹◃for ▹◃ ϵ {≤, <,≥,>}, whose semantics is given by using a membership distance function (mdf). A membership distance function m assigns to each domain element and concept a distance value expressing how "close" is such element to being an instance of the concept. Based on this, a threshold concept C_▹◃tis interpreted as the set of all domain elements that have a distance s from C such that s ▹◃ t. We provide a framework to obtain membership distance functions based on functions that compare tuples of languages, and we show how weighted looping tree automata over a semiring can be used to define membership distance functions for FL₀concepts.