Fuzzy semistar operations on integral domains

In this paper, we introduce the notion of fuzzy semistar operation on an integral domain and relate it to the existing notion of fuzzy star operation. We show that the set of all fuzzy semistar operations on the integral domain is a complete lattice. We also characterize when an overring of a domain is a Prüfer domain and when an overring is a flat module over the domain in terms of a fuzzy semistar operation.