This paper considers a relationship between fuzzy sets and algebraic hyperstructures. A generalization of ideas presented by Davvaz [B. Davvaz, Fuzzy H v -submodules, Fuzzy Sets Syst. 117 (2001) 477–484] and Bhakat and Das [S.K. Bhakat, P. Das, (∈,∈∨q)-fuzzy subgroup, Fuzzy Sets Syst. 80 (1996) 359–368], is presented. In fact, the main purpose of this paper is to introduce and study a new sort of fuzzy H v -submodule of an H v -module called (∈,∈∨q)-fuzzy H v -submodules. These fuzzy H v -submodules are characterized by their level H v -submodules. The concept of a fuzzy H v -submodule with thresholds is introduced, and some interesting properties are investigated.