A hybrid approach to modeling input variables in non-singleton type-2 Fuzzy Logic Systems

The vast majority of fuzzy logic systems and applications employ singleton fuzzification because of its simplicity and speed of computation which allows for real time operation. However, using singleton fuzzification assumes that the input measurements are clean signals with no noise or uncertainty associated with them. The vast majority real world applications have high values of noise and uncertainty associated with the sensor and input values. Higher order Fuzzy Logic Systems (FLSs) such as interval type-2 FLSs have been shown to be very well suited to dealing with the high levels of uncertainties present in the majority of real world applications. However, it seems a paradox to use type-2 FLS to handle the encountered uncertainties while assuming that the input values to the type-2 FLS are perfect inputs when considering singleton fuzzification. Hence, we propose a hybrid approach, which employs non-singleton type-2 FLS where the inputs will be modeled by type-2 fuzzy sets to handle the numerical uncertainties, while the antecedent and consequent type-2 fuzzy sets in the type-2 FLS will be used to handle the linguistic uncertainties. One of the main problems in nonsingleton fuzzification is to determine the shape and the parameters of the input variables and things get complicated when employing type-2 fuzzy based input variables. In this paper, we will present a novel method which is data driven to generate interval type-2 fuzzy sets to model the input variables in non-singleton type-2 FLS. The paper will report on various experimental results employing the proposed method to generate type-2 based fuzzy input variables.