Cardinal Fuzzy Quantifiers Based on the Framework of Fuzzy Sets

Cardinal fuzzy quantifiers are important quantifiers in fuzzy information processing. They are applied broadly in daily communications and practical reasoning with natural languages. In this article, a semantic analysis of cardinal fuzzy quantifiers is put forward and extended into fuzzy sets. We provide a formal semantics for cardinal fuzzy quantifiers under the framework of fuzzy sets. And some theorems of their properties, such as monotonicity, intersection and union properties, are proved. In the end, some valid inference schemas of them are discussed.