Fuzzy hyperlattices

In this paper, we introduce the notion of fuzzy hyperlattices and establish connections between fuzzy hyperlattices and hyperlattices. Then we discuss the relations between the weak homomorphism of fuzzy hyperlattices and the weak homomorphism of corresponding hyperlattices. Moreover, we define and analyze the hypercongruence on hyperlattices and the fuzzy (strong) hypercongruence on fuzzy hyperlattices. And we study the interrelation between the (fuzzy) hypercongruence on (fuzzy) hyperlattices and the homomorphism of (fuzzy) hyperlattices. Also, a relation between the fuzzy hypercongruence on fuzzy hyperlattices and the hypercongruence on corresponding hyperlattices is obtained. Finally, we apply the hypercongruence and the fuzzy strong hypercongruence to construct quotient structures of hyperlattices and fuzzy hyperlattices, respectively.

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