Abstract
In this paper, the notion of weak transposition Fn-hypergroups as a subclass of fuzzy transposition n-ary hypergroups (transposition Fn-hypergroups) is introduced and several properties are found and examples are presented. We show that transposition Fn-hypergroups are a generalization of F-polygroups, Fn-polygroups and join Fn-spaces. Finally, we prove that the class of Fn-polygroups and faint regular weak transposition Fn-hypergroups coincide.
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