Redefined fuzzy Hv-submodules and many valued implications

This paper considers a relationship between fuzzy sets and algebraic hyperstructures. A generalization of ideas presented by Davvaz [B. Davvaz, Fuzzy Hv-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 Hv-submodule of an Hv-module called (∈, ∈ ∨ q)-fuzzy Hv-submodules. These fuzzy Hv-submodules are characterized by their level Hv-submodules. The concept of a fuzzy Hv-submodule with thresholds is introduced, and some interesting properties are investigated.