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Top1. Introduction
Natural-Inspired Optimization Algorithms (NIOAs) (Dhal, Das, Ray et al, 2020; Dhal, Das, Ray et al, 2021; Dhal, Ray, Das, & Das, 2019) have been proposed as an alternative to conventional mathematical approaches for solving complex optimization problems. These techniques are used in Artificial Intelligence (AI) mechanisms, in which a population works together to solve a problem. This inspiring nature has piqued the interest of many researchers who abstract natural phenomena in computational terms to solve complex engineering problems by adapting human collaboration to create NIOA operators and alternative mechanisms for solving them. A plethora of NIOAs have recently been created, based not only on natural laws but also on physical, social, and biological principles (Dhal, Das, Ray et al, 2020; Dhal, Ray, Das, & Das, 2019). The No Free Lunch Theorem (NFL) states that no single optimization algorithm can solve any optimization task (Dhal, Das, Ray et al, 2020; Dhal, Ray, Das, & Das, 2019). This justifies the creation of a large number of NIOAs. As a result, the output of NIOAs is highly dependent on the problem to be solved as well as the structure of the algorithm in question. In this context, the development of novel NIOAs is an accessible and exciting research area, as many issues such as the balance between exploration and exploitation stages, self-adaptivity, parameter-less results, and convergence continue to perplex the NIOAs community. Cuckoo Search Algorithm (CSA) (Yang & Deb, 2009) is a simple and efficient NIOA that has shown to be successful on a variety of optimization tasks. However, the efficacy of CSA is strongly influenced by the capacity for discovery and exploitation, and it may be possible to improve its performance by solving complex optimization problems. There is no interaction or knowledge sharing between solutions in traditional CSA, and only Lévy flight with a fixed step size has been used for exploration and exploitation (Dhal, Das, Ray et al, 2019; Dhal & Das, 2017; Dhal et al., 2017). As a result, researchers are able to effectively develop the CSA by using various methods to address the aforementioned issues. Parameter adaptation (Mareli & Twala, 2018), integration of different random number generators (Yang & Deb, 2009), communication and sharing of information (Dhal, Das, Ray et al, 2019; Dhal et al., 2017; Yang & Deb, 2009), global and local search strategies (Dhal, Das, Ray et al, 2019; Dhal & Das, 2017), hybridization with other NIOA (Chi et al., 2019; Zhang et al., 2019), and initial population development, adaptive population size (Dhal, Das, Sahoo et al, 2021; Dhal et al., 2017; Mlakar et al., 2016), etc are some important strategies to boost the CSA. Parameter adaptation methods, including population size, have a significant impact on the efficiency of the CS algorithm (Mlakar et al., 2016). Particle Swarm Optimizer (PSO) (Abdelbar et al., 2005; Gaxiola et al., 2019; Nobile et al., 2018), Bat Algorithm (BA) (Pérez et al., 2015a; Pérez et al., 2015b), Firefly Algorithm (FA) (Hassanzadeh & Kanan, 2014), and CS (Guerrero et al., 2015; Yang & Deb, 2009) also have used fuzzy logic to derive the rules for parameter adaptation. In this research, fuzzy logic has been applied in a unique way. The population has been divided into two fuzzy sets, each of which has some belongingness, which is determined by the solution's fitness. The solutions are improved by using fuzzy set centroids, global best solution guidance, and Lévy distribution dependent mutation. The validation of the proposed fuzzy CS has been performed over CEC-2014 test suite (Liang et al., 2014) and multi-level thresholding (Dhal, Das, Ray et al, 2020) based image segmentation field with the assistance of well-known objective functions.