The notion of inclusion is one of the most basic relations between sets, however, there is not a consensus about how to extend such a notion in fuzzy set theory. We introduce an alternative approach to previous methods in the literature in which we make use of the so-called φ-index of inclusion. This approach has a main difference with respect to previous ones: instead of a value in [0, 1], the measure of inclusion is identified with a function. In this paper, using the φ-index of inclusion we define two measures of inclusion in the standard sense, i.e., taking a value in [0, 1] and then, we show that both measures are in accordance with the standard axiomatic approaches about measures of inclusion in the literature.