Comparative measures of aggregated uncertainty representations
Uncertainty must be taken into account in all aspects of ambient intelligence and human decisions and activities. We investigate how to utilize both probabilistic and possibilistic sources of information for use in humanized decision-making. In particular we examine aspects of the possibilistic conditioning of probability developed by Yager. To provide bounding of the resulting probability analysis of the cases of completely certain and uncertain probability and possibility distribution are carried out. Additionally the cases of intermediate uncertainty and a general case of possibilities are analyzed. The Zadeh consistency measure is also used to assess these cases. To consider whether the conditioned probability is more informative for decision-making, three measures, Shannon entropy, Gini index and Renyi entropy are used to compare the original probability distributions and the conditioned distribution for the cases described.
possibilistic conditioning consistency measures shannon entropy gini index renyi entropy information theory decision making possibility theory