Comparing apples and oranges through partial orders: An empirical approach

Abstract

In this paper, we try to understand what people mean when they say that two objects are ldquosimilar.rdquo This is an important question in the area of human-robot interactions, where robots must interpret human movements in order to act in a ldquosimilarrdquo manner. Specifically, we assume that we are given a collection of empirically generated pairwise comparisons between a subset of so-called alternatives (members of a given set), which produces a partial order over the set of alternatives. Based on this partial order, an inverse optimization problem is solved, producing a cost associated with each alternative that is consistent with the partial order. This cost is, moreover, assumed to be generative in that it can be used to select the globally best alternative. An experimental study involving the comparison of apples and oranges is presented to highlight the operation of the proposed approach.