A Combinatorial-Probabilistic Diagnostic Entropy and Information

TL;DR

This paper introduces a new combinatorial-probabilistic diagnostic entropy measure that quantifies system uncertainty and diagnosis complexity, providing explicit assessment of symptom information and demonstrating additivity, with potential applications beyond diagnosis.

Contribution

It proposes a novel combinatorial-probabilistic entropy measure for diagnosis, defining symptom information and proving its additivity, applicable to decision theory and classification.

Findings

The new entropy measures system uncertainty and diagnosis complexity.

Explicit formulas for assessing symptom information are derived.

Proven additivity property of the combinatorial-probabilistic information.

Abstract

A new combinatorial-probabilistic diagnostic entropy has been introduced. It describes the pair-wise sum of probabilities of system conditions that have to be distinguished during the diagnosing process. The proposed measure describes the uncertainty of the system conditions, and at the same time complexity of the diagnosis problem. Treating the assumed combinatorial-diagnostic entropy as a primary notion, the information delivered by the symptoms has been defined. The relationships have been derived to facilitate explicit, quantitative assessment of the information of a single symptom as well as that of a symptoms set. It has been proved that the combinatorial-probabilistic information shows the property of additivity. The presented measures are focused on diagnosis problem, but they can be easily applied to other disciplines such as decision theory and classification.