Saeed Mirvakili - Department of Mathematics, Payame Noor University, Tehran, Iran
Sayed Hossein Ghazavi - Department of Mathematics, University of Shahid Ashrafi Esfahani, P.O.Box ۸۱۷۹۸-۴۹۹۹۹, Esfahan, Iran

EL-hypergroups  were defined by Chvalina ۱۹۹۵. Till now, no exact statistics of EL-hypergroups have been done. Moreover, there is no classification of EL-hypergroups and EL^۲-hypergroups even over small sets. In this paper we classify all EL-(semi)hypergroups over sets with two elements obtained from quasi ordered semigroups. Also, we characterize all quasi ordered H_v-group and   then we enumerate the number of EL^۲-H_v-hypergroups and EL^۲-hypergroups of order ۲.

Ends lemma, EL-hypergroups, H_v-group, quasi order relation, partially order relation