Design of an interval Type-2 fuzzy model with justifiable uncertainty

Abstract

Throughout previous design proposals of Interval Type-2 Fuzzy Logic Systems most of the research work concentrates on optimal design to best fit data behavior and rarely focus on the inner model essence of Type-2 Fuzzy Systems, which is uncertainty. In this way, failing to focus on this key aspect, which is how much uncertainty exists within the model to better represent the data. In this paper a design methodology for a Mamdani based Interval Type-2 Fuzzy Logic System (MAM-IT2FLS) with Center-Of-Sets defuzzification is presented, using descriptive statistics and granular computing theory to better define the limits of uncertainty within the Interval Type-2 Membership Functions (IT2MF) as extracted from available data. This allows us to justify the uncertainty within the entire Type-2 Fuzzy Logic model, as well as to create the fuzzy model using FCM grouping and to compute IT2MF parameters from MAM-IT2FLS rules using simple steps. This is unlike hybrid learning models with Back-Propagation that adjust IT2MF parameters with gradient based numeric optimization algorithms which are time efficient but unstable for convergence, and evolutionary computation with robust convergence and slow learning time. Experimentation is carried out with six regression benchmark datasets, measuring RMSE and R2 in order to evaluate the performance of the proposed methodology whilst maintaining justifiable uncertainty in its model.