On the properties of measure in the theory of intermediate quantifiers and the quantifier "Many"

This paper is a contribution to the formal theory of intermediate quantifiers (linguistic expressions such as most, few, almost all, a lot of, many, a great deal of, a large part of, a small part of). This concept informally introduced by Peterson was formalized in the frame of higher-order fuzzy logic by Novak. We address the concept of measure, namely we introduce modified definition providing its additivity and apply the theory to the intermediate quantifier "Many". We show that the ambiguous behavior of it can be also formally substantiated.