Drawbacks of Uncertainty Measures Based on the Pignistic Transformation

Recently, a measure of "total uncertainty" (TU) in Dempster-Shafer theory, based on the pignistic distribution called ambiguity measure (AM), have been modified. The resulting new measure has been simply referred as modified AM (MAM). In the literature, it has been shown that AM, in addition to showing some undesirable behaviors, has important drawbacks related to two essential properties for such measures: 1) subadditivity and 2) monotonicity. The MAM measure has been developed to solve the AM subadditivity problem, but this paper demonstrates that MAM suffers the same drawback as AM with respect to monotonicity. A measure of uncertainty that cannot meet the monotonicity requirement has an important drawback for its exploitation in operational contexts such as in analytics, information fusion, and decision support. This paper aims at identifying and discussing drawbacks of this type of measures (AM, MAM). Our main motivation is to insist upon the important requirement of monotonicity that a TU measure should possess to improve its potential of being used and trusted in applications. This discussion is due time since the monotonicity problem needs first to be solved to avoid building too high expectations for usefulness and potential exploitation of such measures in operational communities.