American Journal of Applied Mathematics
Volume 3, Issue 2, April 2015, Pages: 75-80
Received: Feb. 15, 2015;
Accepted: Feb. 25, 2015;
Published: Apr. 2, 2015
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Slah Benyoussef, Airport Rd, Al-Imam Muhammad Ibn Saud Islamic University, Riyadh 11432, Arabie Saoudite; Faculté des Sciences Economiques et de Gestion de Sfax, route Aéroport km 4, BPN°1088, 3018 Sfax, Tunisie
In many real applications, the data of classification problems cannot be precisely measured. However, in an increasingly complex environment, these variables can be imprecise, qualitative or linguistic. In such a case, fuzzy set theory seems to be the convenient tool to fill this insufficiency. Thus, we proposed a new approach, based on the ranking function, which consists in solving the classification problems via fuzzy linear programming model. This approach has been applied for the financial distress firms. The obtained results are satisfactory in terms of correctly classified rates
Clustering Problem with Fuzzy Data: Empirical Study for Financial Distress Firms, American Journal of Applied Mathematics.
Vol. 3, No. 2,
2015, pp. 75-80.
B. Hasan and al., “An experimental comparison of the new goal programming and the linear programming approaches in the two-group discriminant problems”, Computers & Industrial Engineering vol 50, pp.296-311, 2006.
C. T. Ragsdale and A. Stam, “Mathematical programming formulations for the discriminant problem: an old dog does new tricks”, Decision Sciences vol 22, pp. 296-307, 1991.
D. D. Smith and D. M. Whitt, “Estimating soil losses from field areas of claypan soils”, Soil Science Society of America Proceedings Vol. 12, pp. 485-490, 1947.
D. F. Jones and al., “A classification model based on goal programming with non-standard preference functions with application to the prediction of cinema-going behaviour”, European Journal of Operational Research vol 177, pp.515-524, 2007.
F. Housseinzadeh Lotfi and B. Mansouri, “The extended data envelopment analysis/discriminant analysis approach of fuzzy models”, App Math Sci, Vol 2, N° 29-32, pp.1465-1477, 2008.
F. Glover and al., “A new class of models for the discriminant problem”, Decision Sciences vol 19, pp.269-280, 1988.
G. J. Koehler and S. S. Erenguc S. S, “Minimizing misclassifications in linear discriminant analysis”, Decision Sciences vol 21, pp. 63-85, 1990.
J.J. Glen, “A comparison of standard and two-stage mathematical programming discriminant analysis methods”, European Journal of Operational Research vol 171, pp.496-515, 2006.
L. Zadeh, “Fuzzy sets”, Information and Control Vol 8, pp. 338-353, 1965.
N. Freed and F. Glover, “A linear programming approach to the discriminant problem”, Decision Sciences vol 12, pp.68-74, 1981
N. Freed and F. Glover, “Resolving certain difficulties and improving the classification power of LP discriminant analysis formulations”, Decision Sciences vol 17, pp. 589-595, 1986.
N. Freed and F. Glover, “Simple but powerful goal programming models for discriminant problems”, European Journal of operational research vol 17, pp.44-60, 1981.
P. Markowski and C. A. Markowski, “Some difficulties and improvements in applying linear programming formulations to the discriminant problem”, Decision Sciences vol 16, pp.237-247, 1985.
R. A. Fisher, “The use of multiple measurements in taxonomic problems”, Ann. Eugenics, vol 7, pp.179-188, 1936.
R. Nath and T.W. Jones, “A variable selection criterion in linear programming approaches to discriminant analysis”, Decision Sciences vol 19, pp.554-563, 1988.
S. Bajgier and A. Hill, “An experimental comparison of statistical and linear programming approaches to the discriminant problem”, Decision Sciences vol 13, pp.604-618, 1982.
W. V. Gehrlein, “General mathematical programming formulations for the statistical classification problem”, Operations Research Letters vol 5, N°6, pp. 299-304, 1986.
Alaleh Maskooki, “ Improving the efficiency of a mixed integer linear programming based approach for multi-class classification problem”, Computers & Industrial Engineering, Vol 66, Issue 2, pp. 383-388, 2013
Leandro C. Coelho, Gilbert Laporte, “ Classification, models and exact algorithms for multi-compartment delivery problems”, European Journal of Operational Research, Vol 242, Issue 3, pp. 854-864, 2015
Alireza Nazemi, Mehran Dehghan, “ A neural network method for solving support vector classification problems”, Neurocomputing, Vol 152, Issue 25, pp. 369-376, 2015
Karim Ben Khediri, Lanouar Charfeddine, Slah Ben Youssef, “ Islamic versus conventional banks in the GCC countries: A comparative study using classification techniques”, Research in International Business and Finance, Vol 33, pp.75-98, 2015
Xiao-bin Zhi, Jiu-lun Fan, Feng Zhao, “Fuzzy Linear Discriminant Analysis-guided maximum entropy fuzzy clustering algorithm”, Pattern Recognition, Vol 46, Issue 6, pp. 1604-1615, 2013
Xiaoning Song, Zi Liu, Xibei Yang, Jingyu Yang, “A fuzzy supervised learning method with dynamical parameter estimation for nonlinear discriminant analysis”, Computers & Mathematics with Applications, Vol 66, Issue 10, pp. 1782-1794, 2013