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.