Pure and Applied Mathematics Journal
Volume 7, Issue 2, April 2018, Pages: 11-19
Received: May 30, 2018;
Accepted: Jun. 25, 2018;
Published: Jul. 17, 2018
Views 1016 Downloads 79
Joseph Gogodze, Institute of Control System, Techinformi, Georgian Technical University, Tbilisi, Georgia
This study proposes a game-theoretic approach to solve a multiobjective decision-making problem. The essence of the method is that a normalized decision matrix can be considered as a payoff matrix for some zero-sum matrix game, in which the first player chooses an alternative and the second player chooses a criterion. Herein, the solution in mixed strategies of this game is used to construct a weighted sum of the primary criteria that leads to a solution of the primary multiobjective decision-making problem. The proposed method leads to a notionally objective weighting method for multiobjective decision-making and provides “true weights” even in the absence of preliminary subjective evaluations. The proposed new method has a simple application. It can be applied to decision-making problems with any number of alternatives/criteria, and its practical realization is limited only by the capabilities of the solver of the linear programming problem formulated to solve the corresponding zero-sum game. Moreover, as observed from the solutions of the illustrative examples, the results obtained with the proposed method are quite appropriate and competitive.
Using a Two-Person Zero-Sum Game to Solve a Decision-Making Problem, Pure and Applied Mathematics Journal.
Vol. 7, No. 2,
2018, pp. 11-19.
Marler, R. T., & Arora, J. S. Function-transformation methods for multi-objective optimization. Engineering Optimization, 37(6), 2005, pp. 551-570.
Neumann, Von J. & Morgenstern O. Theory of Games and Economic Behaviour. Princeton University Press, Princeton, NJ, 1944.
Marler, R. T. & Arora, J. S., The weighted sum method for multi-objective optimization: new insights. Structural and multidisciplinary optimization, 41(6), 2010, pp. 853-862.
Farag, M. M. Quantitative methods of materials selection. In: Kutz M, editor. Handbook of materials selection; 2002.
Chatterjee, P., Athawale, V. M., and Chakraborty, S. Selection of materials using compromise ranking and outranking methods. Materials & Design, 30(10), 2009, 4043-4053.
Khabbaz, R., Sarfaraz, B., Dehghan Manshadi, A., Abedian, and R. Mahmudi. A simplified fuzzy logic approach for materials selection in mechanical engineering design. Materials & design 30(3), 2009, pp. 687-697.
Jahan, A., Mustapha, F., Ismail, M. Y., Sapuan, S. M., and Bahraminasab, M. A comprehensive VIKOR method for material selection. Materials & Design, 32(3), 2011, pp. 1215-1221.
Karande, P., and Chakraborty, S. Application of multi-objective optimization on the basis of ratio analysis (MOORA) method for materials selection. Materials & Design 37, 2012, pp. 317-324.
Yazdani, M. New approach to select materials using MADM tools. International Journal of Business and Systems Research, 12(1), 2018, pp. 25-42.
Anyfantis, K., Foteinopoulos, P. and Stavropoulos, P. Design for manufacturing of multi-material mechanical parts: A computational based approach. Procedia CIRP, 66, 2017, pp. 22-26.
Deng, H., Yeh, C. H., & Willis, R. J. Inter-company comparison using modified TOPSIS with objective weights. Computers & Operations Research, 27(10), 2000, pp. 963-973.
El Gibari, S., Gómez, T. and Ruiz, F. Building composite indicators using multicriteria methods: a review. Journal of Business Economics, 2018, pp. 1-24.
Shih, H. S., Shyur, H. J., & Lee, E. S. An extension of TOPSIS for group decision making. Mathematical and Computer Modelling, 45(7-8), 2007, pp. 801-813.
Kusumawardani, R. P. and Agintiara, M. Application of fuzzy AHP-TOPSIS method for decision making in human resource manager selection process. Procedia Computer Science, 72, 2015, pp. 638-646.