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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 condition with transitivity of ξ α . Article Informationdoi:10.52547/hatef.jahla.2.2.35 fatcat:c3kydazekbcq3gexbu7nfwq3we