Comparative conditional possibilities

Any dynamic decision model or procedure for acquisition of knowledge must deal with conditional events and should refer to (not necessarily structured) domains containing only the elements and the information of interest. We consider conditional possibility theory as numerical reference model to handle uncertainty and to study binary relations, defined on an arbitrary set of conditional events expressing the idea of "no more possible than". We give the necessary conditions for the representability of a relation by a T-conditional possibility, for any triangular norm T, and we provide a complete characterization in terms of necessary and sufficient conditions for the representability by a conditional possibility (i.e. when T is the minimum)