Clustering algorithms create groups of objects based on their similarity. As objects are usually defined by data points, this similarity is commonly measured by a distance function. When the objects are defined by variables that are intervals, it is more difficult to determine how to measure the similarity between the objects of the dataset. In this work, we propose some similarity measures between intervals based on average embedding functions. Using these, new similarity measures between interval-based objects are proposed. All the proposed similarities are based on measuring the similarity between the objects variable by variable and then averaging the obtained results to get a single value. By its definition, the objects can be considered as interval-valued fuzzy sets (IVFS), so the similarities introduced are proved to be valid similarities for IVFS. The measures proposed are used in a hierarchical clustering algorithm with the aim of grouping the objects of the dataset into different clusters based on their similarity to interval-valued data. The described process is applied to real data regarding the Spanish weather in order to cluster the provinces of Spain based on the interval temperature of each month in 2021, showing different results that the ones obtained using non-interval-valued data.