Ordinal relative belief entropy

TL;DR

This paper introduces a novel ordinal relative belief entropy that measures uncertainty in a sequence of propositions within a frame of discernment, addressing the limitations of traditional entropies that ignore order effects.

Contribution

The paper proposes a new ordinal entropy that considers the order of propositions, filling a gap in uncertainty measurement for dynamic, sequential processes.

Findings

The proposed entropy effectively captures the impact of proposition order on uncertainty.

Numerical examples verify the correctness and validity of the new entropy.

The method provides a more realistic measure of uncertainty in dynamic decision processes.

Abstract

Specially customised Entropies are widely applied in measuring the degree of uncertainties existing in the frame of discernment. However, all of these entropies regard the frame as a whole that has already been determined which dose not conform to actual situations. In real life, everything comes in an order, so how to measure uncertainties of the dynamic process of determining sequence of propositions contained in a frame of discernment is still an open issue and no related research has been proceeded. Therefore, a novel ordinal entropy to measure uncertainties of the frame of discernment considering the order of confirmation of propositions is proposed in this paper. Compared with traditional entropies, it manifests effects on degree of uncertainty brought by orders of propositions existing in a frame of discernment. Besides, some numerical examples are provided to verify the correctness and validity of the proposed entropy in this paper.