The perspective adopted to evaluate Higher Education Institutions (HEI) depends on the aims of the assessment. The literature proposes several approaches for the HEI evaluation and there are intense debates over which are the most appropriate. In this context, ranking schemes are becoming very popular. However, rankings are mainly slanted towards research and overlook important aspects of universities such as structural differences. Furthermore, depending on the indicator applied, university rankings change, which has been used to delegitimise them. In this framework, we try to gain an insight into the evaluation of HEI applying multivariate methods, to find out whether HEI can be classified into different clusters related to, at least, their three main missions (teaching, research and knowledge transfer), and fuzzy cluster analysis to find out whether HEI can be in different clusters at the same time depending on their degree of belonging to each cluster. Our analysis focuses on the Spanish HES. This study demonstrates that the evaluation of HEI is complex than just rank universities in one-dimensional ranking, given the multiple objectives of HEI. Not all universities plan their strategies in the same way and evaluations should take account of these differences.