A type 2 adaptive fuzzy inferencing system

Type 2 fuzzy sets allow for linguistic grades of membership and, therefore, present a better representation of the `fuzziness´, when applied to a particular problem, than type 1 fuzzy sets. However, the associated cost is that the fuzzy membership grades and rules have somehow to be determined and no recognised approach yet exists. For type 1 systems a number of approaches have been adopted. One in particular is the adaptive network based fuzzy inferencing system (ANFIS) which has successfully been applied to a variety of applications. ANFIS takes domain data and learns the membership functions and rules for a type 1 fuzzy inferencing system. Our work aims to extend this approach for type 2 systems. Our Type 2 adaptive fuzzy inferencing system has inputs that are linguistic variables and the membership functions for these fuzzy grades are learnt from the relationship between these inputs and the given output. The paper describes the algorithm developed highlighting the theoretical and computational issues involved