Total uncertainty of possibility assignments

Recently a measure of uncertainty for general evidence assignments was proposed by N.R. Pal et al. Called total uncertainty, it combines both the dispersion and nonspecificity aspects of uncertainty. The author studies this measure in the context of possibilistic assignments. He establishes its maximum value and the maximizing assignment, and compares it to the traditional possibilistic measure, U-uncertainty. It is shown that in the main, it can be approximated by the sum of separate maxima of information, one computed according to possibilistic, and the other according to probabilistic rules. This is in contrast with earlier measures, which address the extent of conflict among the focal sets, and become negligible for possibilistic assignments. The study thus offers additional support to the thesis that possibility assignments address issues of specificity, while probability assignments deal primarily with dispersion