Interval fuzzy sets allow us to deal not only with vagueness (lack of sharp class boundaries), but also with uncertainty (lack of information). The aim of this tutorial is to present some basic concepts about interval fuzzy numbers. Several concepts related to fuzzy sets are extended to the interval approach. We present an algebraic and ordered structure of interval fuzzy numbers, where the arithmetic operations are defined in terms of interval cuts, allowing the analysis of the properties of the operations based on the properties of the interval arithmetic operations.