Complex Entropy and Its Application in Decision-Making for Medical Diagnosis

Area of Science:

• Information Theory
• Decision Sciences
• Applied Mathematics

Background:

• Measuring uncertainty in complex-valued distributions is a significant challenge in decision-making systems.
• Existing methods struggle with information processing on complex planes.

Purpose of the Study:

• To propose a new complex entropy measure for quantifying uncertainty in complex-valued distributions.
• To develop a multisource information fusion algorithm based on the proposed complex entropy for decision-making.
• To validate the practicability of the developed algorithm in a medical diagnosis context.

Main Methods:

• Generalization of Gini entropy to create a complex entropy measure.
• Analysis of the properties of the proposed complex entropy (nonnegativity, boundedness, etc.).
• Development of a multisource information fusion algorithm utilizing the complex entropy.

Main Results:

• The proposed complex entropy effectively measures uncertainty in complex-valued distributions.
• The complex entropy degrades to Gini entropy for standard probability distributions.
• Numerical examples demonstrate the superiority of the new complex entropy measure.
• The developed decision-making algorithm shows practical applicability in medical diagnosis.

Conclusions:

• The novel complex entropy provides a robust method for uncertainty quantification in complex systems.
• The developed information fusion algorithm enhances decision-making capabilities, particularly in complex-valued data scenarios.
• The application in medical diagnosis highlights the practical utility and effectiveness of the proposed approach.