A variable selection method for a hierarchical interval type-2 TSK fuzzy inference system

Abstract

In this paper, we propose a method to judge the degree of the relationship closeness between system input variables and theoretical output through independence test, and apply this method to construct a hierarchical interval type-2 Takagi-Sugeno-Kang (TSK) fuzzy inference system. Interval type-2 TSK fuzzy inference systems have been applied in many fields. An interval type-2 fuzzy inference system, which is a special case of generalized type-2 fuzzy inference systems, can reduce the computational complexity of type-reduction and save computational cost. An hierarchical fuzzy system can further reduce the complexity of systems. However, it is found that, with the increase in data dimensions, the computational complexity and error of the system will increase. The system accuracy of a hierarchical fuzzy system is also found related to the order of its input variables. Variable selection can select meaningful input variables to decrease input space dimensions, and sort the input variables in some way. This paper proposes a variable selection and sorting method based on independence test. Firstly, input variables data and theoretical output data are classified and contingency tables are established. Chi-square statistics of the contingency tables are calculated for independence test, and input variables that are not independent of theoretical output are selected. Then, the total inertia of the contingency tables is calculated to represent the degree of the relationship closeness between input variables and theoretical output. According to the total inertia, the input variables are sorted and entered the system in order. The proposed method and the model built by the method are tested by dealing with regression problems. By comparing the proposed method on several types of systems, the hierarchical interval type-2 TSK inference system shows a better performance. Then the model is compared with other advanced fuzzy models and non-fuzzy models. Experiments show that its performance is better than the rest.