Jointly continuous multi-utility representations of non-total preorders

In the present paper, dealing with non-total preorders, we are interested in the problem of the existence of multi-utility representations that are jointly continuous in both agents and commodities. Non-total preorders are more realistic to explain the behavior of an individual. Indeed, a decision maker may be incapable or unwilling to compare all feasible alternatives. We study the continuous multi-utility representation of a non-total preorder. This kind of representation is more functional than the classical Richter–Peleg utility representation as it allows a complete characterization of the preorder. Our representation theorems are proved in submetrizable k_ω-consumption spaces.