Interval-valued grey (hyper) group

In this research, we apply the notations of the kernel and relative measure of an interval-valued grey to introduce grey groups (groups are based on interval-valued grey) and grey hypergroups (hypergroups are based on interval-valued grey). The primary method used in this research is based on linear inequalities related to elements of grey (hyper)groups and (hyper)groups. It found a relation between grey hypergroups and grey groups via the fundamental relation and proves that the identity element of any given group plays a main role in the grey groups and show that its measure is greater than or equal to its degree of greyness and less than or equal to its kernel, respectively. We show that any given grey group is a generalization of a group and analyze that interval-valued grey groups are different from the interval-valued fuzzy group.