Graded cube of opposition and its generalized syllogisms with intermediate quantifiers

摘要

In real world, interpretation of natural data using a natural language is very popular. In our previous papers, we introduced mathematical definitions of generalized intermediate quantifiers, which were used for an analysis of natural data using fuzzy association rules. The main approach of this paper is to define new forms of intermediate quantifiers forming a general cube of opposition and applying the theory of syllogistic reasoning to derive new information which is not included in real data.