Generalized information theory for hints

Abstract

This paper develops a new uncertainty measure for the theory of hints that complies with the established semantics of statistical information theory and further satisfies all classical requirements for such a measure imposed in the literature. The proposed functional decomposes into conversant uncertainty measures and therefore discloses a new interpretation of the latters as well. By abstracting to equivalence classes of hints we transport the new measure to mass functions in Dempster-Shafer theory and analyse its relationship with the aggregate uncertainty, which currently is the only known functional for the DempsterShafer theory of evidence that satisfies the same set of properties. Moreover, the perspective of hints reveals that the standard independence notion in Dempster-Shafer theory called non-interactivity corresponds to an amalgamation of probabilistic independence and qualitative independence between frames of discernment. All results in this paper are developed for arbitrary families of compatible frames generalizing the very specialized multi-variate systems that are usually studied in information theory.

An Algebraic Theory of Information: An Introduction and Survey

“…Random maps are also related the Theory of Hints [63] and finally also to Probabilistic Argumentation Systems [64]. Finally, from the point of view of measuring information content, this probabilistic approach puts also Shannon's theory of information in a more general perspective, see [65] for a preliminary discussion. Much remains to be done here.…”

Entropy and Quantity of Information in Technical Designations

“…Теорія натяків зараз розвивається як розгалуження теорії доказів Демпстера-Шейфера [12], і від неї очікують відображення простору ймовірності в звичайну систему розпізнавання [13]. Розглянемо на прикладі, які можливості відкриваються у застосуванні теорії натяків при розгляді нашого прикладу позначення.…”

A new definition of entropy of belief functions in the Dempster–Shafer theory

“…Pouly et al Pouly et al [38] define entropy of a "hint" associated with a BPA m. A hint is a formalization of the multivalued mapping semantics for BPAs, and is more fine-grained than a BPA. Formally, a hint H = (Ω 1 , Ω 2 , P, Γ) consists of two state spaces Ω 1 and Ω 2 , a PMF P on Ω 1 , and a multivalued mapping Γ :…”

“…One method for defining entropy of a BPA m is to first transform the BPA to a corresponding PMF P m , and then use Shannon's entropy of P m as the entropy of m (see, e.g., [31,17,4,22,38]). However, there are many ways to make such a transformation.…”