Shadowed Type-2 Fuzzy Sets in Dynamic Parameter Adaption in Cuckoo Search and Flower Pollination Algorithms for Optimal Design of Fuzzy Fault-Tolerant Controllers

Abstract

In recent, various metaheuristic algorithms have shown significant results in control engineering problems; moreover, fuzzy sets (FSs) and theories were frequently used for dynamic parameter adaption in metaheuristic algorithms. The primary reason for this is that fuzzy inference system (FISs) can be designed using human knowledge, allowing for intelligent dynamic adaptations of metaheuristic parameters. To accomplish these tasks, we proposed shadowed type-2 fuzzy inference systems (ST2FISs) for two metaheuristic algorithms, namely cuckoo search (CS) and flower pollination (FP). Furthermore, with the advent of shadowed type-2 fuzzy logic, the abilities of uncertainty handling offer an appealing improved performance for dynamic parameter adaptation in metaheuristic methods; moreover, the use of ST2FISs has been shown in recent works to provide better results than type-1 fuzzy inference systems (T1FISs). As a result, ST2FISs are proposed for adjusting the Lèvy flight (P) and switching probability (P′) parameters in the original cuckoo search (CS) and flower pollination (FP) algorithms, respectively. Our approach investigated trapezoidal types of membership functions (MFs), such as ST2FSs. The proposed method was used to optimize the precursors and implications of a two-tank non-interacting conical frustum tank level (TTNCFTL) process using an interval type-2 fuzzy controller (IT2FLC). To ensure that the implementation is efficient compared with the original CS and FP algorithms, simulation results were obtained without and then with uncertainty in the main actuator (CV1) and system component (leak) at the bottom of frustum tank two of the TTNCFLT process. In addition, the statistical z-test and non-parametric Friedman test are performed to analyze and deliver the findings for the best metaheuristic algorithm. The reported findings highlight the benefits of employing this approach over traditional general type-2 fuzzy inference systems since we get superior performance in the majority of cases while using minimal computational resources.