Operations on Fuzzy Relations: A Tool to Construct New Hyperrings
Irina Cristea and Sanja Jancic-Rasovic
The key objective of this note is to construct new hyperstructures, in particular hyperrings and Hv-rings, starting from a semigroup endowed with two L-fuzzy relations. We provide sufficient conditions such that the associated hyperstructures, obtained using the union, intersection, composition, Cartesian product of fuzzy relations, are strongly distributive hyperrings or distributive Hv-rings. Finally we discuss on some converse problems, supposing that the hyperstructure associated with the union, or composition of two fuzzy relations is a strongly distributive hyperring and finding condition such that the hyperstructure associated with one of the two fuzzy relations is a strongly distributive hyperring, too.
Keywords: Hyperring; Hv-ring; fuzzy relation.
AMS Mathematics Subject Classification: 20N20, 03E72