Type 〈1,1〉 fuzzy quantifiers determined by fuzzy measures on residuated lattices. Part III. Extension, conservativity and extensionality

We study the properties of extension, conservativity and extensionality of fuzzy quantifiers of type 〈1,1〉 defined using fuzzy measures and integrals. The property of extension states that truth values of quantifier applications are invariant with respect to possible extensions of the universe. Conservativity expresses the property that quantifiers are sensitive in their second argument only to objects that lie in the intersection of their arguments. Extensionality represents a form of the smoothness of quantifiers. We characterize these properties by the corresponding properties of functionals used in the definition of fuzzy quantifiers.