Abstarct: Aabstract‎ In the past, the strong law of large numbers and the central limit theorem for compact sets, as well as independent and identically distributed‏ fuzzy random variables in Banach space have been studied. In recent years, fuzzy metric space and fuzzy ‎normed‎ space have been introduced. When fuzzy uncertainty is greater than random uncertainty, the fuzzy metric space is more useful than the ‎probability‎ metric space. ‎‎Therefore, in this research, we seek to investigate limit theorems in fuzzy normed space in two general cases. In the first case, we examine the law of large numbers for random sets and compact random sets in fuzzy metric space, then express this theorem in situations where our random variables are fuzzy.‎ Given the application of the strong law of large numbers in the bootstrap sampling method, as a practical example the strong law of large numbers theorem expressed for random sets and fuzzy random variables will be used in the bootstrap sampling.‎ ‎‎Also as another application, we will use the proposed fuzzy metric and the strong law of large numbers in bootstrap sampling to reduce noise in image processing. ‎‎‎