The aim of this paper is to investigate the lattices of group fuzzy congruences and normal fuzzy subsemigroups on E-inversive semigroups. We prove that group fuzzy congruences and normal fuzzy subsemigroups determined each other in E-inversive semigroups. Moreover, we show that the set of group t-fuzzy congruences and the set of normal subsemigroups with tip t in a given E-inversive semigroup form two mutually isomorphic modular lattices for every t∈ [0,1].
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