00859nas a2200181   4500000000100000008004100001260000900042653002100051653002300072653001700095653002800112100001600140700002000156245008400176300001000260490000700270520040000277       2022                            d  c202210abelief functions10aconvex combination10ainequalities10ameasures of uncertainty1 aJean Dezert1 aAlbena Tchamova00aOn Inequalities Bounding Imprecision and Nonspecificity Measures of Uncertainty  a37-510 v523 a<p>This article presents proof of two inequalities about two measures of uncertainty of basic belief assignments, called respectively Imprecision measure and U-uncertainty measure, that have been introduced by Dubois and Prade in the 1980s. These inequalities have been considered as obvious by the authors, but to prove them rigorously requires some effort, as demonstrated in this article.</p>