The theory of hyperstructures, started in 1934, uses the multivalued operations or hyperoperations. The fundamental relations connect, by quotients and partitions, this theory with the corresponding classical one. T. Vougiouklis in 1990 was introduced the H_v-structures, the largest class of hyperstructures, by defining the weak axioms where the non-empty intersection replaces the equality. The number of H_v-structures defined on a set, is extremelly greater than the number of the ordinary structures and the classical hyperstructures defined on the same set. This fact leads the H_v-structures to admit more applications and, moreover, change the philosophy of finding the appropriate structure. Specifically, we reduce the number of special H_v-structures if we have more axioms, restrictions and properties. For this, we claim that the H_v-structures are more appropriate models to express theories as the Lie-Santilli’s admissibility.

Hv-structures have lot applications in mathematics and in other sciences. These applications range from biomathematics -conchology, inheritance- and hadronic physics or on leptons, in the Santilli’s iso-theory, to mention but a few. This theory, moreover, is closely related to fuzzy theory; consequently, can be widely applicable in linguistic, in sociology, in industry and production, too. In this presentation we focus on Lie-Santilli’s admissible theory especially on the Hypernumbers or H_v-numbers. Special H_v-fields, the e-hyperfields, can be used, as isofields or genofields, in such way they should cover additional properties and satisfy more restrictions.