Three Group Classification Problem Approach Based on Fuzzy Goal Programming

In this study, a new fuzzy logic and mathematical programming based model was proposed to solve three-group classification problem. Determination of cut-off value, which corresponds to discrimination axis in classification problems, has importance. Status of the cut-off value such as asymmetric triangle fuzzy number, trapezoid fuzzy number and gauss fuzzy number was examined. The proposed approach displayed better performance when compared to Fisher's Linear Discriminant Function and some mathematical programming-based models by using three group data sets used frequently in the literature.

Anahtar Kelimeler:

Three group classification problem, fuzzy logic, mathematical programming, goal programming

Three Group Classification Problem Approach Based on Fuzzy Goal Programming

Keywords:

fuzzy logic, Three group classification problem, mathematical programming, goal programming,

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[1] Fisher, R.A., “The use of multiple measurements in taxonomy problems”, Annals of Eugenics, 7, 179-188, (1936).
[2] Smith, C. A., “Some examples of discrimination”, Annals of Eugenics, 13(1), 272-282, (1946).
[3] Freed, N. & Glover, N.,”A linear programming approach to the discriminant problem”, Decision Sciences, 12, 68-74, (1981).
[4] Stam, A. & Ragsdale, C.T., “On the classification gap in mathematical programming-based approaches to the discriminant problem”, Naval Research Logistics, 39, 545-559, (1992).
[5] Rosen, J.B.,” Pattern separation by convex programming”, Journal of Mathematical Analysis and Applications, 10, 123-134, (1965).
[6] Mangasarian O., “Linear and Nonlinear Separation of patterns by Linear Programming”, Operations Research, 13, 444-452, (1965).
[7] Smith, F.W. “Pattern classifier design by linear programming”, IEEE Transactions on Computers, C-17 (4), 367-372, (1968).
[8] Grinold, R.C.,” Mathematical programming methods for pattern classification”, Management Sciences, 19, 272-289,(1972).
[9] Bajgier, S. M.& Hill, A. V.,” An experimental comparison of statistical and linear programming approaches to the discriminant problem”, Decision Sciences, 13, 604–618, (1982).
[10] Lam, K.F., Moy, J.W., “An experimental comparison of some recently developed linear programming approaches to the discriminant analysis”, Computers and Operations Research, 24(7), 593-599, (1997).
[11] Glen, J. J.,” Integer programming methods for normalisation and variable selection in mathematical programming discriminant analysis models”, Journal of Operational Research Society, 50, 1043–1053, (1999).
[12] Lam, K.F., Choo, E.U., Moy, J.W.,” Minimizing deviations from the group mean: A new linear programming approach for the two-group classification problem”, European Journal of Operational Research, 88,358-367, (1996).
[13] Bal, H., Örkcü, H.H., Çelebioğlu S., “An alternative model to Fisher linear programming approaches in two-group classification problem: Minimizing deviations from the group median”, G.U. Journal of Science, 19(1): 49–55 (2006).
[14] Bal, H., Örkcü, H.H., Çelebioğlu S., “An experimental comparison of the new goal programming and linear programming approaches in the two-group discriminant problems”, Computers&Industrial Engineering, 50(3): 296–311 (2006).
[15] Gehrlein, W.V., ”General mathematical programming formulations for the statistical classification problem”, Operations Research Letters, 5,299-304, (1986).
[16] Choo, E.U., Wedley, W.C., “Optimal criterion weights in repetitive multicriteria decision making”, Journal of Operational Research Society, 36: 983-992, (1985).
[17] Lam, K.F., Moy, J.W., “Improved linear programming formulations for the multi group discriminant problem”, Journal of Operational Research Society, 47: 1526-1529 (1996).
[18] Lam, K.F., Choo, E.U., Moy, J.W., "Minimizing deviations from the group mean: A new linear programming approach for the two-group classification problem", European Journal of Operational Research, 88,358-367, (1996).
[19] Örkcü, H. H., & Bal, H., “A combining mathematical programming method for multi-group data classification”, Gazi University Journal of Science, 24(1), 77–84, (2011).
[20] Youssef, S. B., Jbir, R., & Rebai, A., “A three-group discrimination using new linear programming model”, International Journal of Operational Research, 12(3), 279-293, (2011).
[21] Smaoui, S. & Aouni, B.,” Fuzzy goal programming model for classification problems”, Ann Oper Res, 251:141–160, (2017).
[22] Doğan, M. I., Orman, A., Örkcü, M., & Örkcü, H. H., “A new approach based on regression analysis and mathematical programming to multi-group classification problems”, Journal Of The Faculty Of Engıneering And Architecture Of Gazi University, 34(4), 1939-1955, (2019).
[23] Zadeh, L.A., “Fuzzy Sets”, Information and Control, 8 (3), 338-353, (1965).
[24] Narasimhan, R., “Goal programming in a fuzzy environment”, Decision sciences, 11(2), 325-336, (1980).
[25] Hannan, E. L., “On fuzzy goal programming”, Decision sciences, 12(3), 522-531, (1981).
[26] Li, A., Shi, Y., & He, J., “A data classification method based on fuzzy linear programming”, In MCDM 2006, Chania, Greece, July 19–23, (2006).
[27] Hosseinzadeh, L. F., Jahanshahloo, G. R., Rezai, B. F., & Zhiani, R. H., “Discriminant analysis of imprecise data”, Applied Mathematical Sciences, 1(15), 723–737, (2007).
[28] Hosseinzadeh, L. F., & Mansouri, B.,”The extended data Envelopment analysis/discriminant analysis approach of fuzzy models”, Applied Mathematical Sciences, 2(30), 1465–1477, (2008).
[29] Ben Youssef, S., & Rebai, A., “Discriminant analysis using linear programming models”, International Journal of Knowledge Management Studies, 2(4), 455–459, (2008).