L-fuzzy quantifiers of type 〈1〉 determined by fuzzy measures

The aim of this paper is, first, to introduce two new types of fuzzy integrals, namely, ⊗-fuzzy integral and →-fuzzy integral. The first integral is based on a fuzzy measure of L-fuzzy sets and the second one on a complementary fuzzy measure of L-fuzzy sets, where L is a complete residuated lattice. Some of their properties and a relation to the fuzzy (Sugeno) integral are investigated. Second, using these integrals, two classes of monadic L-fuzzy quantifiers of type 〈1〉 are defined. These L-fuzzy quantifiers can be used for modeling the semantics of natural language quantifiers like “all”, “some”, “many”, “none”, “at most half”, etc. Several semantic properties of these L-fuzzy quantifiers are studied.