Abstract
PROMETHEE methods based on the outranking relation theory are extensively used in multicriteria decision aid. A preference index representing the intensity of preference for one pattern over another pattern can be measured by various preference functions. The higher the intensity, the stronger the preference is indicated. In contrast to traditional single-layer perceptrons (SLPs) with the sigmoid function, this paper develops a novel PROMETHEE II-based SLP using concepts from the PROMETHEE II method involving pairwise comparisons between patterns. The assignment of a class label to a pattern is dependent on its net preference index, which the proposed perceptron obtains. Specially, this study designs a genetic-algorithm-based learning algorithm to determine the relative weights of respective criteria in order to derive the preference index for any pair of patterns. Computer simulations involving several real-world data sets reveal the classification performance of the proposed PROMETHEE II-based SLP. The proposed perceptron performs well compared to the other well-known fuzzy or non-fuzzy classification methods.
Similar content being viewed by others
References
Kim D, Bang SY (2000) A handwritten numeral character classification using tolerant rough set. IEEE Trans Pattern Anal Mach Intell 22(9):923–937
Beltratti A, Margarita S, Terna P (1996) Neural networks for economic and financial modelling. International Thomson Computer Press, London
Hu YC, Tseng FM (2007) Functional-link net with fuzzy integral for bankruptcy prediction. Neurocomputing 70(16–18):2959–2968
Perny P (1998) Multicriteria filtering methods based on concordance and non-discordance principles. Ann Oper Res 80:137–165
Doumpos M, Zopounidis C (2002) Multicriteria decision aid classification methods. Kluwer Press, Dordrecht
Doumpos M, Zopounidis C (2004) A multicriteria classification approach based on pairwise comparisons. Eur J Oper Res 158(2):378–389
Yoon KP, Hwang CL (1995) Multiple attribute decision making: an introduction. Sage Publications, London
Roy B (1995) The outranking approach and the foundations of ELECTRE methods. Theor Decis 31:49–73
Roy B (1968) Classement et choix en présence de points de vue multiple (la méthode Electre). Revue d’Informatique et le Recherche Opérationelle 8:57–75
Brans JP, Marechal B, Vincke Ph (1984) PROMETHEE: a new family of outranking methods in multicriteria analysis. Oper Res 84:477–490
Brans JP, Vincke Ph (1985) A preference ranking organization method. Manag Sci 31(6):647–656
Brans JP, Vincke B, Marechal Ph (1986) How to select and how to rank projects: the PROMETHEE method. Eur J Oper Res 24(2):228–238
Vincke P (1992) Multicriteria decision aid. Wiley, New York
Albadvi A, Chaharsooghi SK, Esfahanipour A (2007) Decision making in stock trading: an application of PROMETHEE. Eur J Oper Res 177(2):673–683
Yan J, Dagang T, Yue P (2007) Ranking environmental projects model based on multicriteria decision-making and the weight sensitivity analysis. J Syst Eng Electron 18(3):534–539
Hermans C, Erickson J, Noordewier T, Sheldon A, Kline M (2007) Collaborative environmental planning in river management: an application of multicriteria decision analysis in the White River Watershed in Vermont. J Environ Manag 84(4):534–546
Zopounidis C, Doumpos M (2002) Multicriteria classification and sorting methods: a literature review. Eur J Oper Res 138(2):229–246
Mahmoud MR, Garcia L (2000) Comparison of different multicriteria evaluation methods of the Red Bluff Diversion Dam. Environ Model Softw 15(5):471–478
Brans JP, Mareschal B (2005) PROMETHEE methods. In: Figueira J, Greco S, Ehrgott M (eds) Multiple criteria decision analysis: state of the art surveys. Springer, Berlin, pp 163–196
Goldberg DE (1989) Genetic algorithms in search, optimization and machine learning. Addison-Wesley, MA
Man KF, Tang KS, Kwong S (1999) Genetic algorithms: concepts and designs. Springer, London
Rooij AJF, Jain LC, Johnson RP (1996) Neural network training using genetic algorithms. World Scientific, Singapore
Olson DL (2001) Comparison of three multicriteria methods to predict known outcomes. Eur J Oper Res 130:576–587
Hu YC (2009) Bankruptcy prediction using ELECTRE-based single-layer perceptron. Neurocomputing 72(13–15):3150–3157
Tseng FM, Lin L (2005) A quadratic interval logit model for forecasting bankruptcy. Omega 33(1):85–91
Osyczka A (2002) Evolutionary algorithms for single and multicriteria design optimization. Physica, NY
Grabisch M, Dispot F (1992) A comparison of some methods of fuzzy classification on real data. In: Proceedings of the 2nd International Conference on Fuzzy Logic and Neural Networks. Iizuka, Japan, pp 659–662
Weiss SM, Kulikowski CA (1991) Computer systems that learn: classification and prediction methods from statistics, neural nets, machine learning and expert systems. Morgan Kaufmann, San Mateo
Hu YC (2007) Fuzzy integral-based perceptron for two-class pattern classification problems. Inf Sci 177(7):1673–1686
Ishibuchi H, Yamamoto T, Nakashima T (2005) Hybridization of fuzzy GBML approaches for pattern classification problems. IEEE Trans Syst Man Cybern 35(2):359–365
Abonyi J, Roubos JA, Szeifert F (2003) Data-driven generation of compact, accurate, and linguistically-sound fuzzy classifiers based on a decision-tree initialization. Int J Approx Reason 32(1):1–21
Zarndt F (1995) A comprehensive case study: an examination of machine learning and connectionist algorithms. Master thesis, Brigham Young University, Provo
Yousef R, Hindi K (2005) Training radial basis function networks using reduced sets as center points. Int J Inf Technol 2(1):21–35
Altman EL (1968) Financial ratios, discriminant analysis and the prediction of corporate bankruptcy. J Finance 23:596
Zmijewski M (1984) Methodological issues related to the estimation of financial distress prediction models. J Account Res 22(1):59–82
Kuncheva LI (2000) Fuzzy classifier design. Physica, Heidelberg
Ishibuchi H, Nozaki K, Yamamoto N, Tanaka H (1995) Selecting fuzzy if-then rules for classification problems using genetic algorithms. IEEE Trans Fuzzy Syst 3(3):260–270
Ishibuchi H, Nakashima T, Nii M (2004) Classification and modeling with linguistic information granules: advanced approaches to linguistic data mining. Springer, Berlin
Acknowledgments
The authors would like to thank the anonymous referees for their valuable comments. This research is partially supported by Chung Yuan Christian University under grant CYCU-99RD-RA002-11594.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Hu, YC., Chen, HC. Integrating multicriteria PROMETHEE II method into a single-layer perceptron for two-class pattern classification. Neural Comput & Applic 20, 1263–1271 (2011). https://doi.org/10.1007/s00521-010-0424-2
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00521-010-0424-2