Utility Representation of an Incomplete Preference Relation

We consider the problem of representing a (possibly) incomplete preference relation by means of a vector-valued utility function. Continuous and semicontinuous representation results are reported in the case of preference relations that are, in a sense, not “too incomplete.” These results generalize some of the classical utility representation theorems of the theory of individual choice, and paves the way towards developing a consumer theory that realistically allows individuals to exhibit some “indecisiveness” on occasion.