A study on fuzzy reasoning mechanism based on extension principle

The author looks at the possibility to extend precise reasoning based on classical set theory to fuzzy reasoning based on fuzzy set theory by using Zadeh's extension principle. It is shown from the decomposition theorem in fuzzy set theory that the whole fuzziness of an object can be characterized by a sequence of local clear properties of that object. Hence, fuzzy reasoning can also be implemented by using a sequence of precise reasonings. Considering this ideal, we can translate the fuzzy relation "if A then B" in generalized modus ponens (GMP) rule into a corresponding precise relation between subsets of X and subsets of Y, then extend this corresponding precise relation to two kinds of transformations between fuzzy sets of X and fuzzy sets of Y by using of Zadeh's extension principle. Finally, two extension principle-based fuzzy reasoning methods, the GMP and generalized modus tollens fuzzy reasoning methods, are established, and some properties about these two fuzzy reasoning methods investigated.