SCIENCE CHINA Information Sciences, Volume 60 , Issue 8 : 082103(2017) https://doi.org/10.1007/s11432-016-9101-8

## Ordered proposition fusion based on consistency and uncertainty measurements

• AcceptedMay 12, 2017
• PublishedJul 5, 2017
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### Abstract

The fusion of ordered propositions is an important and widespread problem in artificial intelligence, but existing fusion methods have difficulty handling the fusion of ordered propositions. In this paper, we propose a solution based on consistency and uncertainty measurements. The main contributions of this paper are as follows. First, we propose the concept of convexity degree, mean, and center of basic support function to comprehensively describe the basic support function of ordered propositions. Second, we introduce entropy as a measure of uncertainty in the basic support function of ordered propositions. Third, we generalize the indeterminacy of the basic support function and propose a novel method to measure the consistency between two basic support functions. Finally, based on the above researches, we propose a novel algorithm for fusing ordered propositions. Theoretical analysis and experimental results demonstrate that the proposed method outperforms state-of-the-art methods.

• Figure 1

Explanation of negative regulation for basic support function.

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Algorithm 1 Fusion of basic support functions of ordered propositions

Require:Basic support functions $\mu$ and $\nu$, the weights $\Omega _\mu$ and $\Omega _\nu$;

Output:Fusion result $\omega$;

if $\mu \in \Delta$ AND $\nu \in \Delta$ then

$\omega \leftarrow \gamma$;

return

ELSIF $\mu \in \Delta$ AND $\nu \notin \Delta$ $\omega \leftarrow \nu$; ELSIF $\mu \notin \Delta$ AND $\nu \in \Delta$ $\omega \leftarrow \mu$;

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