S. Mirvakili - Department of Mathematics, Payame Noor University, P.O.BOX ۱۹۳۹۵-۳۶۹۷ Tehran, Iran,
S. H. Ghazavi - Department of Mathematics, Shahid Ashrafi Esfahani University, Isfahan, Iran
M. A. Dehghanizadeh - Technical and Vocational University(TVU), Tehran, Iran

EL-hypergroups were defined by Chvalina ۱۹۹۵. Tillnow, 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 withtwo 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