Extensions of fuzzy hyperideals in HV-semigroups

The object of the present paper is the investigation and study of (fuzzy) hyperideals in H-v-semigroups. Regular equivalence relations play in H-v-semigroup theory a role analogous to congruences in semigroup theory, so we introduce fuzzy regular equivalence relations on H-v-semigroups and then we study fuzzy Rees regular relations on H-v-semigroups. Using this ideas, we establish a relation between fuzzy hyperideal of an H (v)-semigroup H and fuzzy hyperideal of a quotient H-v-semigroup of H. Some characterizations of them are then shown.