Godel representable fuzzy weak orders

This paper is devoted to the study of fuzzy weak orders, fuzzy quasi orders and fuzzy quasi-transitive relations in the context of group decision making. Transitivity is modelled by means of the minimum operator. In analogy to the numerical representation of classical weak orders, we consider a particular class of fuzzy weak orders that can be constructed from a numerical evaluation by means of the Godel implicator. We fully characterize the fuzzy relations that can be written as the intersection or union of a finite family of these so-called Godel representable fuzzy weak orders.