On the uniqueness of possibilistic measure of uncertainty and information

Abstract

It is demonstrated, through a series of theorems, that the U-uncertainty (introduced by Higashi and Klir in 1982) is the only possibilistic measure of uncertainty and information that satisfies possibilistic counterparts of axioms of the well established Shannon and hartley measures of uncertainty and information. Two complementary forms of the possibilistic counterparts of the probabilistic branching (or grouping) axiom, which is usually used in proofs of the uniqueness of the Shannon measure, are introduced in this paper for the first time. A one-to-one correspondence between possibility distributions and basic probabilistic assignments (introduced by Shafer in his mathematical theory of evidence) is instrumental in most proofs in this paper. The uniqueness proof is based on possibilistic formulations of axioms of symmetry, expansibility, additivity, branching, monotonicity, and normalization.