Fuzzy structures on hyperK-algebras
In this note first we define the notions of fuzzy hyperK-subalgebra and fuzzy (weak) hyperK-ideal of a hyperK-algebra. Then we state and prove some equivalent conditions for these notions. In particular we conclude that any fuzzy hyperK-ideal is weak but the converse is not correct in general. After that under a suitable condition we show that a fuzzy subset is a fuzzy hyperK-subalgebra if and only if it is a fuzzy weak hyperK-ideal. Also we give a correspondence theorem for fuzzy hyperK-ideals. Finally by considering the notion of fuzzy strongest relation, we state and prove some related results. Also we give many examples throughout the manuscript.
hyperk-algebra fuzzy hyperk-subalgebra fuzzy (weak) hyperk-ideal