TY - JOUR ID - 158476 TI - Interval-valued grey (hyper)group JO - Journal of Algebraic Hyperstructures and Logical Algebras JA - JAHLA LA - en SN - 2676-6000 AU - Hamidi, M. AU - Mirvakili, S. AU - Hatami, A. AD - Payam nor university, Kashan AD - Department of Mathematics, Payame Noor University, P.O. Box 19395-4697, Tehran, Iran AD - Department of Mathematics, Payame Noor University, Tehran, Iran Y1 - 2022 PY - 2022 VL - 3 IS - 3 SP - 85 EP - 96 KW - Interval-valued grey KW - grey group KW - grey hypergroup KW - fundamental relation DO - 10.52547/HATEF.JAHLA.3.3.6 N2 - 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. UR - https://jahla.hatef.ac.ir/article_158476.html L1 - https://jahla.hatef.ac.ir/article_158476_8a86812f772e758af7a9032568aef5a4.pdf ER -