@article{ref1,
title="The centroid or consensus of a set of objects with qualitative attributes",
journal="Expert systems with applications",
year="2011",
author="Guzman-Arenas, Adolfo and Cuevas, Alma-Delia and Jimenez, Adriana",
volume="38",
number="5",
pages="4908-4919",
abstract="It is clear how to compute the average of a set of numeric values; thus, handling inconsistent measurements is possible. Recently, using confusion, we showed a new way to compute the consensus (a kind of average) of a set of assertions about a non-numeric fact, such as the religion of John.This paper solves the same problem for a set of objects possessing several symbolic attributes. Suppose there is a murder, and we ask several observers about the height, sex, hair color and ethnicity of the killer. They report divergent observations. What is the most likely portrayal of the assassin? Given a bag of assertions about an object described by qualitative features, this paper tells how to assess the most plausible or &quot;consensus&quot; object description. It is the most likely description to be true, given the available information. It is the &quot;centroid&quot; of the bag. We also compute the inconsistency of the bag: how far apart the testimonies in the bag are. All observers are equally credible, so differences arise from perception errors, and from the limited accuracy of the individual findings.<p />",
language="",
issn="0957-4174",
doi="10.1016/j.eswa.2010.09.169",
url="http://dx.doi.org/10.1016/j.eswa.2010.09.169"
}