Abstract

In this paper, we determined a new characterisation of the derived nilpotent (Engel) Lie ring of fuzzy hyperrings by fuzzy strongly regular relation (). Moreover, we proved that for a fuzzy hyperring S, the quotient () was a nilpotent (Engel) Lie ring. Also, we introduced the notion of an ζ-role of a fuzzy hyperring and investigated its essential properties. Basically, we stated a necessary and sufficient condition for transitivity of ζ. Also, we studied the relationship between the strongly regular relation and ζ-role of a given fuzzy hyperring.

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