Decision making problem is the process of finding the best option from all of the feasible alternatives. One of the most important concepts in decision making process is to identify the weights of criteria. In real-world situation, because of incomplete or non-obtainable information, the data (attributes) are often not deterministic and can be treated in forms of fuzzy numbers. This paper investigates a method for deriving the weights of criteria from the pair-wise comparison matrix with fuzzy elements. Finding the weights of criteria has been one of the most important issues in the field of decision-making and the present method uses goal programming to solve the resulted model. In addition, using a ranking function we convert each obtained fuzzy weight to a crisp one, which makes it possible to compare the criteria. The proposed model of this paper is supported by several examples and a case study.
DOI: j.msl.2011.10.005 Keywords: Triangular fuzzy number ,Fuzzy pair-wise comparison matrix ,Goal programming ,Ranking function How to cite this paper: Izadikhah, M. (2012). A goal programming method for deriving fuzzy priorities of criteria from inconsistent fuzzy comparison matrices.Management Science Letters, 2(1), 29-42.
References
Abo-Sinna, M.A., & Amer, A.H. (2005). Extensions of TOPSIS for multi-objective large-scale nonlinear programming problems. Applied Mathematics and Computation, 162, 243-256.
Asady, B., & Zendehnam, M. (2007). Ranking of fuzzy numbers by minimize distance, Applied Mathematical Modeling,31, 2589-2598. Bellman, R.E., & Zadeh, L.A. (1970). Decision making in a fuzzy environment. Management Science, 17, 141-164. Barzilai, J. (1997). Deriving weights from pairwise comparison matrices. Journal of Operational Research Society, 48, 1226–1232. Charnes, A., & Cooper, W.W. (1961). Management Model and Industrial Application of Linear Programming, 1st ed., Wiley, New York.Chen, C.T. (2000). Extensions of the TOPSIS for group decision-making under fuzzy environment. Fuzzy Sets and Systems, 114, 1-9. Chen, S. J., & Hwang C. L. (1992). Fuzzy Multiple Attribute Decision Making: Methods and Applications, Springer-Verlag. Berlin. Cogger, K.O., & Yu, P.L. (1985). Eigen weight vectors and least distance approximation for revealed preference in pairwise weight ratios. Journal of Optimization Theory and Applications, 46, 483-491. Crawford, G., & Williams, C.A. (1985). A note on the analysis of subjective judgment matrices. Journal of Mathematical Psychology, 29, 387-405. Geoffrion, A.M., Dyer, J.S., & Feinberg, A. (1972). An interactive approach for multicriterion optimization with an application to operation of an academic department. Management Science, 19, 357-368. Haimes, Y.Y. (1980). The surrogate worth trade-off (SWT) method and its extensions, in: G. Fandel and T. Gal (eds.). Multiple Criteria Decision Making Theory and Application, Springer-Verlag, New York.Hwang C.L., & Yoon K. (1981). Multiple Attribute Decision Making Methods and Applications. Springer, Berlin Heidelberg. Islam, R., Biswal, M.P., & Alam, S.S. (1997). Preference programming and inconsistent interval judgments. European Journal of Operational Research, 97, 53-62. Izadikhah, M. (2009). Using the Hamming distance to extend TOPSIS in a fuzzy environment. Journal of Computational and Applied Mathematics, 231, 200-207. Jahanshahloo, G.R., Hosseinzadeh Lotfi F., Izadikhah M. (2006). An algorithmic method to extend TOPSIS for decision-making problems with interval data. Applied Mathematics and Computation, 175, 1375-1384. Jahanshahloo, G.R., Hosseinzadeh Lotfi, F., & Izadikhah, M. (2006). Extension of the TOPSIS method for decision-making problems with fuzzy data. Applied Mathematics and Computation, 181(2), 1544-1551. Ramik, J., & Korviny, P. (2010). Inconsistency of pair-wise comparison matrix with fuzzy elements based on geometric mean. Fuzzy Sets and Systems,161, 1604-1613. Saaty, T.L. (1980). The Analytic Hierarchy Process, McGraw-Hill, New York.Salo A, & Haimalainen R. (1997). On the measurement of preferences in the analytic hierarchy process. Journal of Multi-Criteria Decision Analysis, 6, 309–319. Takeda, E., Cogger, K.O., & Yu, P.L. (1987). Estimating criterion weights using eigenvectors: A comparative study. European Journal of Operational Research, 29, 360-369.Wang, Y-M. (2006). On lexicographic goal programming method for generating weights from inconsistent interval comparison matrices. Applied Mathematics and Computation, 173, 985-991. Zionts, S., & Wallenius, J. (1976). An interactive programming method for solving the multiple criteria problem. Management Science, 22, 652-663. Zadeh, L.A. (1965). Fuzzy sets. Information and Control, 8, 338-353. |
® 2013 GrowingScience.Com