Leticia Amador-Angulo

This study proposes an enhanced Sugeno–Takagi interval type-2 fuzzy logic system (SIT2FLS) to find the best values for two important parameters in Bee Colony Optimization (BCO). The aim of this study was to develop a stable controller for a mobile robot utilizing BCO in the fuzzy controller and to determine the best membership functions (MFs) in a type-1 fuzzy logic system (T1FLS) for control. Another objective was to use an SIT2FLS to find the best $\alpha$ and $\beta$ parameters for BCO to enhance the robot trajectory, which was evaluated through an analysis of the mean squared errors. Three types of perturbations were analyzed and simulated. The performance of the SIT2FLS-FBCO was evaluated and compared to that of the T1FLS-FBCO. In addition, a comparative study was performed to demonstrate that the improved BCO works well when there are disturbances affecting the controller. Finally, it was compared with the Mamdani approach, and an FBCO with an interval type-3 FLS was also developed.

An enhanced whale optimization algorithm (WOA) through the implementation of a generalized type-2 fuzzy logic system (GT2FLS) is outlined. The initial idea is to improve the efficacy of the original WOA using a GT2FLS to find the optimal values of the ${\overrightarrow{\mathit{r}}}_{\mathbf{1}}$ and ${\overrightarrow{\mathit{r}}}_{\mathbf{2}}$ parameters of the WOA, for the case of optimizing mathematical functions. In the WOA algorithm, ${\overrightarrow{\mathit{r}}}_{\mathbf{1}}$ is a variable that affects the new position of the whale in the search space, in this case, affecting the exploration, and ${\overrightarrow{\mathit{r}}}_{\mathbf{2}}$ is a variable that has an effect on finding the local optima, which is an important factor for the exploration. The efficiency of a fuzzy WOA with a GT2FLS (FWOA-GT2FLS) is highlighted by presenting the excellent results of the case study of the benchmark function optimization. A relevant analysis and comparison with a bio-inspired algorithm based on artificial bees is also presented. Statistical tests and comparisons with other bio-inspired algorithms and the initial WOA, with type-1 FLS (FWOA-T1FLS) and interval type-2 FLS (FWOA-IT2FLS), are presented. For each of the methodologies, the metric for evaluation is the average of the minimum squared errors.

In this paper, an improved whale optimization algorithm (WOA) based on the utilization of an interval type-2 fuzzy logic system (IT2FLS) is presented. The main idea is to present a proposal for adjusting the values of the ${\overrightarrow{r}}_1$ and ${\overrightarrow{r}}_2$ parameters in the WOA using an IT2FLS to achieve excellent results in the execution of the WOA. The original WOA has already proven itself as an algorithm with excellent results; therefore, a wide variety of improvements have been made to it. Herein, the main purpose is to provide a hybridization of the WOA algorithm employing fuzzy logic to find the appropriate values of the ${\overrightarrow{\mathrm{r}}}_1$ and ${\overrightarrow{\mathrm{r}}}_2$ parameters that can optimize the mathematical functions used in this study, thereby providing an improvement to the original WOA algorithm. The performance of the fuzzy WOA using IT2FLS (FWOA-IT2FLS) shows good results in the case study of the benchmark function optimization. An important comparative with other metaheuristics is also presented. A statistical test and the comparative with other bio-inspired algorithms, namely, the original WOA with type-1 FLS (FWOA-T1FLS) are analyzed. The performance index used is the average of the minimum errors in each proposed method.

In this study, the first goal is achieving a hybrid approach composed by an Interval Type-3 Fuzzy Logic System (IT3FLS) for the dynamic adaptation of α and $\beta$parameters of Bee Colony Optimization (BCO) algorithm. The second goal is, based on BCO, to find the best partition of the membership functions (MFs) of a Fuzzy Controller (FC) for trajectory tracking in an Autonomous Mobile Robot (AMR). A comparative with different types of Fuzzy Systems, such as Fuzzy BCO with Type-1 Fuzzy Logic System (FBCO-T1FLS), Fuzzy BCO with Interval Type-2 Fuzzy Logic System (FBCO-IT2FLS) and Fuzzy BCO with Generalized Type-2 Fuzzy Logic System (FBCO-GT2FLS) is analyzed. A disturbance is added to verify if the FBCO-IT3FLS performance is better when the uncertainty is present. Several performance indices are used; RMSE, MSE and some metrics of control such as, ITAE, IAE, ISE and ITSE to measure the controller’s performance. The experiments show excellent results using FBCO-IT3FLS and are better than FBCO-GT2FLS, FBCO-IT2FLS and FBCO-T1FLS in the adaptation of $\alpha$and $\beta$parameters.