Cuckoo Search (CS) algorithm is a nature-inspired optimization algorithm (NIOA) with less control parameters that is stable, versatile, and easy to implement. CS has good global search capabilities, but it is prone to local optima problems. As a result, it may be possible to improve the classic CS algorithm's optimization capability. Centered on fuzzy set theory, this paper introduces an improved CS version. The population of solutions has been divided into two fuzzy sets, and each solution is assigned to one of the sets based on its fitness. The fuzzy collection centroids, global best solution advice, and Lévy distribution dependent mutation are all used to boost the population's solutions. With well-accepted objective functions such as Otsu inter class variance and Kapur's entropy, the experimental analysis has been conducted on the CEC-2014 test suite and image multi-level thresholding domain. The proposed fuzzy cuckoo search (FCS) algorithm is compared to the classical CS, PSO, FA, SMA, and BA algorithm and provides satisfactory results.