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In recent years, new metaheuristic algorithms have been developed taking as reference the inspiration on biological and natural phenomena. This nature-inspired approach for algorithm development has been widely used by many researchers in solving optimization problems. These algorithms have been compared with the traditional ones and have demonstrated to be superior in many complex problems. This paper attempts to describe the algorithms based on nature, which are used in optimizing fuzzy clustering in real-world applications. We briefly describe the optimization methods, the most cited ones, nature-inspired algorithms that have been published in recent years, authors, networks and relationship of the works, etc. We believe the paper can serve as a basis for analysis of the new area of nature and bio-inspired optimization of fuzzy clustering. [ABSTRACT FROM AUTHOR]