Dang Julong introduced the Grey system theory in 1982. Following that, in 2011, Yingje Yang proposed Grey sets. Maurice Frechet, a French Mathematician, pioneered the study of Metric space in 1905. A metric is a function that calculates the distance between any two elements of a set. Grey sets can be thought of as an extension to fuzzy sets if characteristic function values are limited to values between [0, 1]. The ordered pair ((U),d) forms a metric space and is called a Grey metric space. The application of grey sets in metric space as a mathematical tool can help solve issues with unclear and uncertain data. In this study, we speculated about how Grey metric space is used in real-life situations. Here, we create an algorithm to calculate the maximum possible distance between the two grey sets and discuss under the topic "Application in Grey Metric Space".In this paper, we also demonstrated its effectiveness with examples

Grey numbers, Grey sets, Grey metric space, Distance