Studying On Inference Engine And Type-reducer Of A Type-2 Fuzzy System

Type-2 fuzzy set is introduced as the extension of type-1 fuzzy set, which has two membership grades. Type-2 fuzzy set increases the fuzziness in description and increases the ability to handle inexact information. In this paper, the definition and the computational properties of type-2 fuzzy set were discussed. We present the structure of type-2 fuzzy logic system and we especially focus on the inference engine and type-reducer.Many properties of type-2 fuzzy sets are extended from type-1. For one thing, Zadeh extension principle makes sense in the process of extending the computation and centroid from type-1 to type-2. For the other, the embedded type-2 fuzzy sets can also extend the computation to type-2, the result being exactly the same as the result derived from the extension principle. In this paper, using the embedded type-2 fuzzy sets to drive the centroid of type-2 is also introduced, the result being also exactly the same as the result drived from extension principle.Type-2 fuzzy logic system inherits many characteristics of type-1 fuzzy logic system. Due to type-2 fuzzy sets participate in every module of type-2 fuzzy logic system. The process of the modules in type-2 are not exactly the same as the modules in type-1, especially the fuzzy inference engine and type-reducer.In type-1 fuzzy logic system, the input and output of fuzzy inference are type-1 fuzzy set. In type-2 case, the input and output are type-2 fuzzy set. Because of the huge computational difference between type-1 and type-2, the process of the inference engine is also different. In this paper, Kleene-Dienes, Lukasiewicz, Zadeh and Reichenbach inference operators are extended to type-2 case. Then we implemented them in type-2 fuzzy inference engine and also testified the justifiability of these operators.The calculation of type-reducer in type-2 fuzzy logic system is quite complex, which limits the use of type-2 fuzzy logic system. Hence, the researchers focus on how to build a simple method to type-reduce. Based on the methods that already have, this paper introduces two approximate ways to type-reduce. Even though both of these two methods are approximations, not the exact result, they can still reduce the computational complexity by large and they are quite useful in practical application.