This dissertation research investigates, using the generalized Hartley measure of nonspecificity (GH(m) = [special characters omitted] m(A) lg | A |), the meaning and applicability of the three principles of nonspecificity (minimum, maximum, and invariance of nonspecificity) within the uncertainty theories subsumed under the Dempster-Shafer formalism.

The Principle of Minimum Nonspecificity was applied to the three problem areas of simplification, conflict resolution, and reconstructability analysis. Possibilistic systems, those based on the Dempster-Shafer theory of evidence, and joint bodies of evidence were examined. Solutions to conflict resolution problems were obtained via linear optimization problems, and reconstruction problem of Reconstructability Analysis was explored within the context of Dempster-Shafer theory.

It was shown that while the lower and upper probabilities of lambda measures always qualify as reachable, the distributions are not identical with those obtained by the calculus of reachable interval-valued probabilities.

Missing or incomplete information problems were also explored. Here the application of the maximum nonspecificity principle generated "linear programming" scenarios.

An algorithm to approximate Dempster-Shafer Theory uncertainty via k-Order Additive Measure approximations was devised and applied to example scenarios.

The Principle of Nonspecificity Invariance was applied to transforming (based only on Hartley nonspecificity) probability distributions to and from possibility profiles.

Uncertainty invariance was also employed to approximate evidence theory uncertainty by possibility measures. If the body of evidence was not nested, the interactive representation lattice would provide candidates for possible scaling to achieve desired approximations, but was found applicable only if downward scaling is possible.