Fuzzy $H_V$-substructures in a two dimensional euclidean vector space

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In this paper, we study fuzzy substructures in connection with $H_{v}$-structures. The original idea comes from geometry, especially from the two dimensional Euclidean vector space. Using parameters, we obtain a large number of hyperstructures of the group-like or ring-like types. We connect, also, the mentioned hyperstructures with the theta-operations to obtain more strict hyperstructures, as $H_{v}$-groups or $H_{v}$-rings (the dual ones).