In this paper, we introduce a new class of (semi)hypergroup from a given (partially) quasi-ordered (semi) hypergroup as a generaliza- tion of "El-Hyperstructures". Then, we study some basic properties and important elements belong to this class.

The Lie-Santilli admissible theory gives in physics applications mainly in producing energy. The mathematical models need to be multivalued and the class of Hv-structures is the most appropriate, since this is the largest class of hyper-structures. The Hv-numbers, weak hyper-numbers, used satisfy all needed axioms. We focus on small and very-thin Hv-fields with P-hyper-operations on the product.

A salt metathesis reaction is a chemical process involving the exchange of bonds between two reacting chemical species, which results in the creation of products with similar or identical bonding affiliations. Hyperstructure theory is studied from the theoretical point of view and for its applications. In this paper, we provide some examples of Hyperstructures associated with salt metathesis reactions, and we observe that these chemical reactions are examples of the phenomena when composition of two elements is a set of elements.

Algebraic Hyperstructures represent a natural extension of classical algebraic structures and they have many applications in various sciences. In this paper, we investigate mathematical structures of chemical reactions for arbitrary elements with four oxidation states.

EL-hypergroups were defined by Chvalina 1995. Till now, no exact statistics of EL-hypergroups have been done. Moreover, there is no classification of EL-hypergroups and EL2-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 charac-terize all quasi ordered Hv-group and then we enumerate the number of EL2-Hv-hypergroups and EL2-hypergroups of order 2.