On Engel Fuzzy Subpolygroups
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 μ of P and β*, the fundamental relation on a given polygroup P, we construct an Engel fuzzy subgroup μβ*. We obtain a necessary and sufficient condition between Engel fuzzy subpolygroups and the Engel group P/∼, the group of equivalence classes derived from a fuzzy subpolygroup of P. Finally, by using these results, we get Zorn’s lemma, in the Engel fuzzy subpolygroups.