Concepts, rules, and fuzzy reasoning: a factor space approach

The representation of knowledge (concepts, facts, and rules) is discussed. In the representation schema, the main tools used are factors spaces and fuzzy sets. Factors are used to capture the characteristics of a concept (intension), and fuzzy sets are used to describe the membership degree of objects to a concept (extension). Various forms of facts and rules are presented in the factor space structure. Fuzzy reasoning is discussed. The nature of fuzzy reasoning is analyzed by dissecting a fuzzy rule in two different ways. By using level cuts of rules and classic implications, some implication operators are obtained. Some reasoning principles are provided in factor spaces