Fuzzy measures; fuzzy integrals; L-fuzzy quantifiers; qualitative integrals; graded square of opposition; modern square.

Qualitative or equivalently fuzzy integrals are used as qualitative aggregation functions or as L-fuzzy quantifiers. In both cases they are generalisations of Sugeno integrals. The definitions of these fuzzy integrals are quite similar and coincide in particular cases, but surprisingly there is no deeper analysis of their relationship. The paper attempts to fill this gap and provides unified definitions of fuzzy quantifiers on the basis of which various links between these fuzzy integrals are studied. In order to make these links more visible and to emphasise their logical structure, we present them using the graded square and modern square of opposition.