%0 Journal Article %T On $\alpha$-solvable fundamental groups %J Journal of Algebraic Hyperstructures and Logical Algebras %I University of Hatef (Hatef College University) %Z 2676-6000 %A Mohammadzadeh, F. %A Mohammadzadeh, E. %D 2021 %\ 05/01/2021 %V 2 %N 2 %P 35-46 %! On $\alpha$-solvable fundamental groups %K Fuzzy hypergroup %K fundamental relation %K $alpha$-solvable group %R 10.52547/HATEF.JAHLA.2.2.35 %X We introduce a specific kind of equivalence relation ${\xi^*}_n^{\alpha}$ on a fuzzy hypergroup S such that the quotient $S/ {\xi^*}_n^{\alpha}$, the set of all equivalence classes, is an $\alpha$-solvable group. This helps us to introduce the $\alpha$-solvable fundamental relation $\xi^{*\alpha}$. In particular, we obtain an equivalent condition with transitivity of $\xi^\alpha$. %U https://jahla.hatef.ac.ir/article_132755_745d49519fe12905cc1c482af9c1f924.pdf