Representations on Raised Very Thin Hv-fields

The hyperstructures have applications in mathematics and other sciences such as biology, physics, linguistics, sociology, to mention but a few. For this, mainly, the largest class of the hyperstructures, the Hvstructures, is used, which satisfy the weak axioms where the non-empty intersection replaces the equality and they are straightly related to fuzzy set theory. The fundamental relations connect the Hv-structures with the classical ones, moreover, they reveal new concepts as the Hv-fields. Hv-numbers are called the elements of an Hv-field and they are used in representation theory. We introduce the raised finite Hv-fields, and present some results and examples on 2 × 2 representations on them.