<p>Where do the three-way decisions and interval sets come from? They are all derived from the lower approximation and upper approximation rough sets. The rough concept is between two approximate sets, that is, some of the uncertainty information can be characterized by interval sets. In the face of interval set information systems, how can we consider and how do we study the corresponding rough sets and three-way decisions? This paper starts from interval sets and their operations, and establishes several rough set models based on interval sets and fuzzy interval sets. These models called interval-set-valued (fuzzy) rough sets are based on the interval set objects and interval set relationships being studied: (1) objects are interval sets, (2) objects are fuzzy interval sets, (3) both objects and relationships are interval sets and (4) both objects and relationships are fuzzy interval sets. This not only provides research methods and ideas for dealing with interval set information systems, but also helps the study of interval sets and rough sets.</p>