A Modular Implementation Scheme for Nonsingleton Type-2 Fuzzy Logic Systems With Input Uncertainties

Abstract

Using nonsingleton (NS) input fuzzifiers along with type-2 fuzzy systems to handle uncertainties in inputs has received some attention in recent years. However, the NS fuzzification schemes proposed so far have a limited impact because they are restricted to a particular kind of fuzzy sets only. This paper proposes a modular implementation scheme for NS type-2 fuzzy logic systems with input uncertainties. The proposed implementation scheme constitutes a generalized fuzzification which is independent of the forms/shapes of the fuzzy sets, i.e., both the NS fuzzifiers and the membership functions. To investigate the effectiveness of the proposed scheme, type-2 fuzzy logic controllers for three different applications, airplane altitude control, obstacle avoidance for a mobile robot, and a wall following robot, are developed. Additionally, for mapping NS fuzzifiers for real sensors, a sensory noise pattern recognition stage is also developed. Despite encountering various kinds of membership functions and input uncertainties along these three applications, the proposed scheme is able to successfully deal with all three applications. Moreover, the performance results in all three application setups show that NS fuzzification can improve the robustness of type-2 fuzzy logic systems against input uncertainties.