Interval-valued grey (hyper)group

Document Type : Original Article


1 Payam nor university, Kashan

2 Department of Mathematics, Payame Noor University, P.O. Box 19395-4697, Tehran, Iran

3 Department of Mathematics, Payame Noor University, Tehran, Iran


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.