Local relations hold reasoning

The fuzzy reasoning system contains more information than its form-generalized modus ponens (GMP), So it´s hard to use GMP as a formal deduction rule directly. In this paper we represent these vague and fuzzy information as relations on concepts, we view rules of fuzzy reasoning system as a mapping from the set of antecedents to the set of consequents, and this mapping holds some relations on antecedents and consequents. Given a premise, we use an extension of the mapping as deduction rule, and this extension holds the relations on the set of antecedents and the set of consequents locally. This reasoning method can be employed to many cases that fuzzy reasoning is applied. We propose a vague knowledge representation framework called pattern classes, and have discussed some useful concepts about vague knowledge representation and reasoning. To some extent, representing fuzzy information as relations on concepts is an orthogonal representation method comparing with fuzzy sets. in many cases this reasoning method can deal with fuzziness without using fuzzy sets theory. It indicates a probability to employ GMP to a formal logic system