Abstract
In this paper, by considering the notions of polygroup and Engel group, we introduce the concept of Engel fuzzy subpolygroups. In this regard, by a normal Engel fuzzy subpolygroup [Formula: see text] of [Formula: see text] and [Formula: see text], the fundamental relation on a given polygroup [Formula: see text], we construct an Engel fuzzy subgroup [Formula: see text]. We obtain a necessary and sufficient condition between Engel fuzzy subpolygroups and the Engel group [Formula: see text]/[Formula: see text], the group of equivalence classes derived from a fuzzy subpolygroup of [Formula: see text]. Finally, by using these results, we get Zorn’s lemma, in the Engel fuzzy subpolygroups.
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