An empirical study of uncertainty measures in the fuzzy evidence theory

Fuzzy evidence theory (FET) extends Dempster-Shafer theory by allowing to represent, within one body of evidence, all three types of uncertainty usually contained within a piece of information: fuzziness, non-specificity, and discord. Two measures have recently been proposed to quantify uncertainty contained in a fuzzy body of evidence, namely General Uncertainty Measure (GM) and Hybrid Entropy (FH). In this paper, we empirically study these uncertainty measures in a Monte-Carlo simulation. To achieve that, we generate random fuzzy bodies of evidence and combine them using three different information fusion rules existing in the FET framework. We observe that on average, the uncertainty gradually decreases when we combine more random fuzzy bodies of evidence together. This observation testifies to the soundness of the examined measures. However, in certain cases, the two measures disagree: while one measure increases between two consecutive fusions, the other one can decrease or remain constant. We analyse such cases using several numerical examples and show that FH can exhibit a counter-intuitive behavior in certain cases. We also compare the two measures in terms of the time required to compute them and conclude that GM is significantly more computationally time-consuming than FH.