Generalized fuzzy HvHv-submodules endowed with interval valued membership functions

We introduce the concept of an interval valued (α,β)(α,β)-fuzzy HvHv-submodule of an HvHv-module. This concept is a generalization of a fuzzy HvHv-submodule of an HvHv-module. In the paper, we investigate interval valued (∈,∈∨q)(∈,∈∨q)-fuzzy HvHv-submodules and present some structural results. We also consider such HvHv-submodules endowed with an implicative operation. Some related results recently obtained by Davvaz, Dudek, Corsini and Jun on HvHv-submodules are extended.