On monotonicity of type 〈1,1〉 fuzzy quantifiers determined by fuzzy measures

In this contribution, we study a very important semantic property of generalized quantifiers called the monotonicity for fuzzy quantifiers of type 〈1,1〉 defined using fuzzy measures and Sugeno type of fuzzy integrals. We show that fuzzy integrals can ensure under some natural conditions the monotonicity of fuzzy quantifiers. Finally, we propose the concept of concave fuzzy quantifiers and prove that each concave fuzzy quantifier is expressible as the conjunction of a non-increasing and a non decreasing fuzzy quantifier.