Abstract
In this paper we introduce and analyze the fundamental relation on fuzzy hyperrings. This relation is the smallest equivalence relation on a given fuzzy hyperring such that it's quotient structure is a ring. Then we introduce the notion of a fuzzy complete part of a fuzzy hyperring and we study the relationship between the fundamental relation and fuzzy complete parts of a fuzzy hyperring. Also the commutative fundamental relation is introduced that its quotient structure in this case is a commutative ring. Finally some necessary and sufficient conditions so that this relation be transitive, are determined.
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