Abstract
In this paper, the notion of a balanced subset of a hypervector space over the field of real numbers is generalized to a hypervector space over an arbitrary valued field. Moreover, absorbing subsets of hypervector spaces are redefined. Next, the concept of balanced fuzzy subsets of hypervector spaces over valued fields is redefined and the balanced hull of fuzzy subsets of hypervector spaces is presented. Also, the notion of absorbing fuzzy subsets of hypervector spaces is introduced and some related results are obtained. Finally, the behavior of the mentioned notions under linear transformations is investigated.
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