Valuation theory on Krasner hyperfields

Valuation theory is an important area of investigation in algebra with applications in algebraic geometry and number theory. In 1957 M. Krasner introduced hyperfields, which are field-like structures with a multivalued addition, to describe some structures arising naturally from valued fields. We would like to discuss the possibility of generalising the notion of valuation to the multivalued setting and the potential that this higher point of view has in the understanding of classical valuation theory. For example, a valuation on a field K is nothing but a homomorphism of hyperfields from K onto a special type of hyperfield, which is called (generalised) tropical hyperfield.