Layer-2 transferable belief model: Manage uncertainty on random permutation sets

Witness	Testimony	Reliability
1	$ {\omega }_{3} $ is more likely to be the perpetrator than $ {\omega }_{1} $.	0.80
2	Likelihood of the perpetrator is $ {\omega }_{3}\succ {\omega }_{2}\succ {\omega }_{1} $.	0.85
3	Perpetrator is $ {\omega }_{3} $ or $ {\omega }_{4} $.	0.30
4	Perpetrator is $ {\omega }_{1} $.	0.50
5	$ {\omega }_{3} $ is more likely to be the perpetrator than $ {\omega }_{4} $.	0.25

Table 2. PerMFs of testimonies and contextual knowledge.

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Table 2. PerMFs of testimonies and contextual knowledge.

Witness	Testimony	Reliability
1	$ \mathrm{P}\mathrm{e}\mathrm{r}{\mathrm{m}}_{{T}_1}\left({F}_{5}^{2}\right)=1.0 $	$ \operatorname{Perm}_{{R}_1}(\varnothing)=0.80{\mathrm{,}} \quad \operatorname{Perm} _{{R}_1}\left(F_{15}^i\right)=\dfrac{0.20}{24}{\mathrm{,}}\; i=\{1{\mathrm{,}}\;2{\mathrm{,}}\; \cdots{\mathrm{,}}\; 24\} $
2	$ \mathrm{P}\mathrm{e}\mathrm{r}{\mathrm{m}}_{{T}_2}\left({F}_{7}^{6}\right)=1.0 $	$ \operatorname{Perm}_{{R}_2}(\emptyset)=0.85{\mathrm{,}}\quad \operatorname{Perm}_{{R}_2}\left(F_{15}^i\right)=\dfrac{0.15}{24}{\mathrm{,}}\; i=\{1{\mathrm{,}}\; 2{\mathrm{,}}\;\cdots {\mathrm{,}}\; 24\} $
3	$ \mathrm{P}\mathrm{e}\mathrm{r}{\mathrm{m}}_{{T}_3}\left({F}_{12}^{1}\right)=0.5 $$ \mathrm{P}\mathrm{e}\mathrm{r}{\mathrm{m}}_{{T}_3}\left({F}_{12}^{2}\right)=0.5 $	$ \operatorname{Perm}_{{R}_3}(\emptyset)=0.30{\mathrm{,}} \quad \operatorname{Perm}_{{R}_3}\left(F_{15}^i\right)=\dfrac{0.70}{24}{\mathrm{,}}\; i=\{1{\mathrm{,}}\; 2{\mathrm{,}}\; \cdots {\mathrm{,}}\; 24\} $
4	$ \mathrm{P}\mathrm{e}\mathrm{r}{\mathrm{m}}_{{T}_4}\left({F}_{1}\right)=1.0 $	$\operatorname{Perm}_{{R}_4}(\emptyset)=0.50{\mathrm{,}} \quad \operatorname{Perm}_{{R}_4}\left(F_{15}^i\right)=\dfrac{0.50}{24}{\mathrm{,}}\; i=\{1{\mathrm{,}}\; 2{\mathrm{,}}\;\cdots {\mathrm{,}}\; 24\} $
5	$ \mathrm{P}\mathrm{e}\mathrm{r}{\mathrm{m}}_{{T}_5}\left({F}_{7}^{1}\right)=1.0 $	$ \operatorname{Perm}_{{R}_1}(\emptyset)=0.25{\mathrm{,}} \quad \operatorname{Perm}_{{R}_5}\left(F_{15}^i\right)=\dfrac{0.75}{24}{\mathrm{,}}\; i=\{1{\mathrm{,}}\;2{\mathrm{,}}\; \cdots {\mathrm{,}}\; 24\} $

Table 3. Parameters of the datasets.
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Table 3. Parameters of the datasets.
Dataset Instance Label Attribute
Iris 150 3 4
Wine 178 3 13
Seed 270 3 7
Breast cancer 569 2 30
Sonar 208 2 60
Iono 351 2 34

Table 4. Comparison of experimental results of three classifiers.

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Table 4. Comparison of experimental results of three classifiers.

Dataset	TBM	RPSR	Layer-2 TBM
Iris	95.29%	95.99%	95.54% (0.25, 1.00, 0.80) 95.61% (0.30, 1.00, 0.80) 95.57% (0.35, 1.00, 0.80)
Wine	97.20%	98.04%	97.55% (0.35, 0.00, 0.80) 97.84% (0.40, 0.00, 0.80) 97.55% (0.45, 0.00, 0.80)
Seed	90.35%	93.40%	91.16% (0.33, 1.00, 0.80) 91.18% (0.33, 1.00, 1.00) 91.35% (0.33, 0.00, 1.00)
Breast cancer	71.71%	73.27%	93.66% (0.20, 0.10, 0.80) 93.93% (0.20, 0.10, 0.50)
Sonar	67.33%	75.39%	69.02% (0.01, 1.00, 0.80) 69.09% (0.01, 0.50, 0.80) 68.38% (0.01, 0.00, 0.80)
Iono	80.86%	87.97%	84.72% (0.01, 0.00, 0.80) 81.55% (0.10, 0.00, 0.80) 82.08% (0.20, 0.00, 0.80)

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Qian-Li Zhou, Yong Deng. Layer-2 transferable belief model: Manage uncertainty on random permutation sets[J]. Journal of Electronic Science and Technology, 2025, 23(2): 100304

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