On qualitative measures of ignorance

Relational structures for measures of ignorance

“…Such characterization A1-A3 of ambiguity has been proved useful with respect to some concepts of Dempster-Shafer's theory of evidence [12], [15], as in the following example. A belief function is a mapping     : 0,1 Bel P X  satisfying the following axioms, for every positive integer n and every collection 12 …”

“…is an ambiguity function [15]. Hence, the greater the interval between plausibility (the amount of information that potentially supports A) and belief (the amount of information that surely supports A), the greater the ignorance due to ambiguity on A there will be.…”

“…Following [4], [15], where crisp ambiguity relations have been defined, an ambiguity relation can be extended to a fuzzy environment as follows. Let be a relation on   f PX .…”

“…The intuition here is that the simplest epistemic attribution for ignorance refers to the absence of relevant knowledge, such that the word ignorance refers to a situation where there is no precise knowledge about a set of objects of interest [15]. Under this view, ignorance can be classified into two epistemic categories, one concerned with the validity of information, i.e., uncertainty, and the other concerned with the exact meaning of information, i.e., ambiguity.…”

“…In order to do so, we now introduce relational structures as it has been done in [15]. For some universe X, where   PX is the set of all subsets of X, i.e., the power set of X, and ¬A stands for the complement of A   PX  , let be a relation on…”