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A new view of fuzzy hyperquasigroups

This paper concerns a relationship between fuzzy sets and algebraic hyperstructures. It is a continuation of ideas presented by Davvaz(Fuzy Sets Syst. 101: 191.195 1999) and Bhakat and Das(Fuzzy Sets Syst. 80: 359.368 1996). The concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set, which is a generalization of quasi-coincidence of a fuzzy point with a fuzzy set, is introduced. Using this new idea, the notion of interval valued (α, β)-fuzzy sub-hyperquasigroups in a hyperquasigroup, which is a generalization of a fuzzy sub-quasigroup, is defined, and related properties are investigated. In particular, the study of interval valued (∈, ∈, ∨q)-fuzzy sub-hyperquasigroups in a hyperquasigroup is dealt with. Finally, we consider the concept of implication-based interval valued fuzzy sub-hyperquasigroups in a hyperquasigroup.