Multi-criteria classification of reward collaboration proposals

Figures & data

Figure 1. Transformation of exact preferences into probabilistic preferences.

Figure 2. Five classes and five criteria with one profile per class.

Figure 3. Allocation of an alternative in one of two classes.

Figure 4. Graphic representation of Choquet integral.

Figure 5. Years in prison of prisoner A.

Figure 6. Absolute differences of the proposals.

Table 1. Characterization of eight Proposals by evaluations according to six criteria.

Proposal	Penalty1	Penalty2	Penalty3	CRIM.ORG	Workload	Consistency
[1]	4	4	4	2	0	2
[2]	6	6	0	1	1	1
[3]	6	0	6	1	1	1
[4]	0	6	6	1	1	1
[5]	12	0	0	1	2	0
[6]	0	12	0	1	2	0
[7]	0	0	12	0	2	0
[8]	2	2	2	0	3	0

Table 2. Translation of evaluations to the interval [0, 1].

Proposal	Penalty1	Penalty2	Penalty3	CRIM.ORG	Workload	Consistency
[1]	1/3	1/3	1/3	1	0	1
[2]	½	1/2	0	1/2	1/3	1/2
[5]	1	0	0	1/2	2/3	0
[7]	0	0	1	0	2/3	0
[8]	1/6	1/6	1/6	0	1	0

Table 3. Scores for the five alternatives based on three criteria.

Class	[1]	[2]	[5]	[7]	[8]
1	0.84	0.61	0.67	0.48	0.26
2	0.64	0.32	0.43	0.24	0.08
3	0.17	0.19	0.00	0.13	0.47
4	0.33	0.62	0.43	0.49	0.75
5	0.63	0.81	0.67	0.71	0.87

Table 4. Classification by different composition rules.

	3			4			5			6
	1^st	2^nd	3^rd	1^st	2^nd	3^rd	1^st	2^nd	3^rd	1^st	2^nd	3^rd
[1]	3	3	3	3	3	3	3	3	3	3	3	3
[2]	3	2	3	3	2	3	3	2	3	3	2	3
[5]	3	3	3	3	3	3	3	3	3	3	3	3
[7]	2	3	3	2	3	3	3	3	3	2	3	3
[8]	2	2	2	2	2	2	2	3	3	2	3	3

Figure 7. Distribution of proposals by classes.

Data availability statement

The data supporting the findings of this study are available within the article and in its supplementary materials.