A novel framework for the implementation and evaluation of type-1 and interval type-2 ANFIS - Chen, Chao (2018)
This thesis explores a novel framework for implementing and evaluating type-1 (T1) and interval type-2 (IT2) models of Adaptive Network Fuzzy Inference Systems (ANFIS). A fundamental requirement for this research is the capability to reliably and efficiently implement ANFIS models. In the last ten years, many studies have been devoted to creating IT2 ANFIS models. However, a clear architecture for IT2 ANFIS has not yet been presented. This somehow has been an obstacle to the research of IT2 ANFIS and its application to real-world problems. In this thesis, we introduce an extended ANFIS architecture that can be used for both T1 and IT2 models. In conjunction with this, a crucial obstacle to the use of IT2 fuzzy systems in general (and including IT2 ANFIS) is that IT2 models are often more computationally expensive than T1 models. Note that a bottle-neck for IT2 ANFIS is to aggregate the output of each rule produced by the inference process of the Karnik-Mendel (KM) algorithm. Many enhanced algorithms have been proposed to improve the computational efficiency of the KM algorithm. However, all of these algorithms are still based on iterative procedures to determine the switch points required for the lower and upper bounds of defuzzification. This thesis introduces a `direct approach' which can be used to determine these switch points based on derivatives, without the need for multiple iterations. When comparing various models (including T1 and IT2 ANFIS models), it is necessary to conduct fair comparisons. Partly to address this issue, a new accuracy measure is proposed which combines the best features of various alternative measures without having their common drawbacks. Experimental comparisons are made between T1 and IT2 ANFIS using the novel accuracy measure in addition to the commonly used RMSE, on both synthetic and real-world data. Finally, it is shown that IT2 ANFIS models are not easy to optimise from scratch due to difficulties with the output intervals, that are not present in T1 ANFIS models. Detailed experiments are carried out to evaluate the comparative performance of IT2 ANFIS models, including the best method for initialising the IT2 membership functions. In summary, a coherent framework for efficiently implementing IT2 ANFIS models and fairly evaluating their comparative performance is presented. This framework allows the implementation of IT2 ANFIS in any application context, and the resultant performance to be carefully considered, since clear performance improvement compared to T1 ANFIS may not always be found.