n α-solvable fundamental groups

We introduce a specific kind of equivalence relation ξ∗α_n on a fuzzy hypergroup S such that the quotient S/ξ∗α_n , the set of all equivalence classes, is an α-solvable group. This helps us to introduce the α-solvable fundamental relation ξ∗α. In particular, we obtain an equivalent con-dition with transitivity of ξα.