Proaftn

Proaftn is a fuzzy classification method that belongs to the class of supervised learning algorithms. The acronym Proaftn stands for: (PROcédure d'Affectation Floue pour la problématique du Tri Nominal), which means in English: Fuzzy Assignment Procedure for Nominal Sorting.

The method enables to determine the fuzzy indifference relations by generalizing the indices (concordance and discordance) used in the ELECTRE III method.^[1] To determine the fuzzy indifference relations, PROAFTN uses the general scheme of the discretization technique described in,^[2] that establishes a set of pre-classified cases called a training set.

To resolve the classification problems, Proaftn proceeds by the following stages:^[3]

Stage 1. Modeling of classes: In this stage, the prototypes of the classes are conceived using the two following steps:

• Step 1. Structuring: The prototypes and their parameters (thresholds, weights, etc.) are established using the available knowledge given by the expert.
• Step 2. Validation: We use one of the two following techniques in order to validate or adjust the parameters obtained in the first step through the assignment examples known as a training set.

Direct technique: It consists in adjusting the parameters through the training set and with the expert intervention.

Indirect technique: It consists in fitting the parameters without the expert intervention as used in machine learning approaches.^[4][5]

In multicriteria classification problem, the indirect technique is known as preference disaggregation analysis.^[6] This technique requires less cognitive effort than the former technique; it uses an automatic method to determine the optimal parameters, which minimize the classification errors.

Furthermore, several heuristics and metaheuristics were used to learn the multicriteria classification method Proaftn.^[7][8]

Stage 2. Assignment: After conceiving the prototypes, Proaftn proceeds to assign the new objects to specific classes.

External links

• Site dedicated to the sorting problematic of MCDA

References

1. Roy, B. (1996). Multicriteria Methodology for Decision Aiding. Dordrecht: Kluwer Academic.
2. Ching, J.Y. "Class-dependent discretization for inductive learning from continuous and mixed-mode data". IEEE Transactions on Pattern Analysis and Machine Intelligence. 7: 641–651. doi:10.1109/34.391407.
3. Belacel, N. (2000). "Multicriteria assignment method PROAFTN: Methodology and medical application". European Journal of Operational Research. 125 (3): 175–83. doi:10.1016/s0377-2217(99)00192-7.
4. Doumpos, M.; Zopounidis, C. (2011). "Preference disaggregation and statistical learning for multicriteria decision support: A review". European Journal of Operational Research. 209 (3): 203–214. doi:10.1016/j.ejor.2010.05.029.
5. Belacel, N.; Rava, H. B.l; Punnen, A. P. (2007). "Learning multicriteria fuzzy classification method PROAFTN from data". Computers & Operations Research. 34 (7): 1885–1898. doi:10.1016/j.cor.2005.07.019.
6. Jacquet-Lagrèze, E.; Siskos, J. (2001). "Preference disaggregation: Twenty years of MCDA experience". European Journal of Operational Research. 130 (2): 233–245. doi:10.1016/s0377-2217(00)00035-7.
7. Al-Obeidat, F.; et al. (2011). "An evolutionary framework using particle swarm optimization for classification method PROAFTN". Applied Soft Computing. 11 (8): 4971–4980. doi:10.1016/j.asoc.2011.06.003.
8. Al-Obeidat, f.; et al. (2010). "Differential Evolution for learning the classification method PROAFTN". Knowledge Based System. 23 (5): 418–426. doi:10.1016/j.knosys.2010.02.003.