Intermetidate quantifiers; fuzzy quantifiers; fuzzy type theory; partial fuzzy logic

This paper is a contribution to the formal theoryof intermediate quantifiers (linguistic expressions such as most,few, almost all, a lot of, many, a great deal of, a large part of, asmall part of ). This concept informally introduced by Petersonwas formalized in the frame of higher-order fuzzy logic bythe author of this paper. The formal theory of intermediatequantifiers is in this paper modified to situations when fuzzysets characterizing properties of elements can be only partiallydefined. The presentation in this paper is purely semantic andprovides also algorithm how intermediate quantifiers can becomputed in a finite model.