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In the Carnot engine, which achieves the maximum efficiency between two reservoirs of fixed temperatures, the total change in entropy is zero. The observation can be generalized by considering any reversible cyclic process consisting of many Carnot cycles. Thus, it can be stated that the total entropy change of any ideal reversible cycle is zero.
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Interval-valued belief entropies for Dempster-Shafer structures.

Yige Xue¹, Yong Deng^1,2,3

¹Institute of Fundamental and Frontier Sciences, University of Electronic Science and Technology of China, Chengdu, 610054 China.

Soft Computing

|June 9, 2021

Summary

This study introduces interval-valued belief entropies for Dempster-Shafer structures, extending existing models to handle uncertainty in evidential environments. This new method effectively quantifies uncertainty for better decision-making.

Keywords:

Belief entropy Dempster–Shafer structures Interval-valued entropies Shannon entropy Uncertainty

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Area of Science:

Uncertainty Quantification
Information Theory
Decision Theory

Background:

Traditional entropy models struggle with complex uncertainty in practical applications.
Yager's interval-valued entropies for Dempster-Shafer structures offer a solution within traditional probability spaces.
Extending these entropies to broader evidential environments remains an open challenge.

Purpose of the Study:

To propose and validate interval-valued belief entropies for Dempster-Shafer structures.
To extend the applicability of interval entropy models to evidential reasoning.
To provide a robust method for quantifying uncertainty in complex scenarios.

Main Methods:

Development of interval-valued belief entropies based on Dempster-Shafer structures.
Mathematical formulation ensuring degeneracy to interval-valued entropies under specific conditions.
Application of numerical examples to demonstrate validity and effectiveness.

Main Results:

The proposed interval-valued belief entropies successfully quantify the interval uncertainty of objects.
The method is shown to be effective in decision-making processes.
Validation through numerical examples confirms the theoretical framework.

Conclusions:

Interval-valued belief entropies offer a significant advancement for uncertainty quantification in evidential environments.
This approach enhances the practical utility of Dempster-Shafer structures.
The findings support improved theoretical research and industrial applications involving complex uncertainty.