Citation: Guerrero, M.; Valdez, F.; Castillo, O. Comparative Study between Type-1 and Interval Type-2 Fuzzy Systems in Parameter Adaptation for the Cuckoo Search Algorithm. Symmetry 2022, 14, 2289. https://doi.org/10.3390/ sym14112289 Academic Editors: Jian-Qiang Wang and José Carlos R. Alcantud Received: 21 September 2022 Accepted: 22 October 2022 Published: 1 November 2022 Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affil- iations. Copyright: © 2022 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). symmetry S S Article Comparative Study between Type-1 and Interval Type-2 Fuzzy Systems in Parameter Adaptation for the Cuckoo Search Algorithm Maribel Guerrero, Fevrier Valdez and Oscar Castillo * Tijuana Institute of Technology, TecNM, Tijuana 22414, Mexico * Correspondence: ocastillo@tectijuana.mx Abstract: The objective of this work is focused on improving the optimization ability of the cuckoo search algorithm (CS), and, for this reason, a comparison is made between type-1 and interval type-2 fuzzy logic to look for more promising results in the cuckoo search algorithm (CS), and to help performance, we dynamically adjust the alpha parameter. The idea is to enable CS in leaving the local optima, and then be able to reach the global optima. Currently, there are good results in improving the optimization of algorithms through intelligent fuzzy logic computing after finding the best adjustment parameters. The approach is based on finding the ideal rules with their respective linguistic variables to represent the real world as is perceived by humans. The membership functions that the fuzzy system uses are symmetrically defined for reducing the search space, and this symmetry is what makes the algorithm efficient. We plan to test the proposal in future works in the optimal design of control systems. In the present study, we use five benchmark mathematical functions with variation in the number of dimensions to validate the approach and perform the comparison of interval type-2 and type-1 fuzzy systems in parameter adaptation. For the dynamic adjustment of the parameters, we select the alpha parameter, and the values of Pa and Beta are defined based on the analysis of their behavior in previous works. Keywords: cuckoo search; interval type-2; type-1 fuzzy system 1. Introduction In our daily life, there are various tasks that make our activities easier; for this, we can perceive something as basic as using a washing machine, a car, a digital camera, an elevator, etc. that allow us to carry out an activity in less time. In all of these examples, we can denote the implementation of soft computing, which is a branch of Artificial Intelligence (AI) that allows us, through mathematical tools, to implement the way in which we, as human beings, process or manage activities or reasons to recognize objects or people and make decisions. Fuzzy logic is a relatively simple method of information processing, decision making, and process control. In this article, we will address the concept of fuzzy logic, the contrast between type-1 and type-2 fuzzy, their basic concepts, and the applications that we can find in mod- ern times. The main motivation of this study is to provide a better performance in CS, and then to be able to be implement in future works in different control systems, contribute to the optimization, and compare the results with other metaheuristics. The idea of fuzzy logic was put forward by Professor L.A. Zadeh of the University of California, Berkeley, in 1965, who published an article called “fuzzy set”, which initiated a new area that is now known worldwide [1,2]. Fuzzy logic has been implemented with bio-inspired algorithms for the optimization of controllers for solving a wide range of problems, such is the case of the galactic swarm algorithm, particle swarm optimization, and hybrid optimization algorithms, in the control Symmetry 2022, 14, 2289. https://doi.org/10.3390/sym14112289 https://www.mdpi.com/journal/symmetry