Intermediate quantifiers in presence of partial fuzzy sets

This paper is a contribution to the formal theory ofintermediate 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 the author of this paper. The formal theory of intermediate quantifiers is in this paper modified to situations when fuzzy sets characterizing properties of elements can be only partially defined. The presentation in this paper is purely semantic and provides also algorithm how intermediate quantifiers can be computed in a finite model.