An extension of TOPSIS for group decision making. (English) Zbl 1187.90166

Summary: An extension of TOPSIS (technique for order performance by similarity to ideal solution), a multi-attribute decision making (MADM) technique, to a group decision environment is investigated. TOPSIS is a practical and useful technique for ranking and selection of a number of externally determined alternatives through distance measures. To get a broad view of the techniques used, we provide a few options for the operations, such as normalization, distance measures and mean operators, at each of the corresponding steps of TOPSIS. In addition, the preferences of more than one decision maker are internally aggregated into the TOPSIS procedure. Unlike in previous developments, our group preferences are aggregated within the procedure. The proposed model is indeed a unified process and it will be readily applicable to many real-world decision making situations without increasing the computational burden. In the final part, the effects of external aggregation and internal aggregation of group preferences for TOPSIS with different computational combinations are compared using examples. The results have demonstrated our model to be both robust and efficient.


90B50 Management decision making, including multiple objectives


Full Text: DOI


[1] Hwang, C. L.; Yoon, K., Multiple Attribute Decision Making (1981), Springer-Verlag: Springer-Verlag Berlin
[2] Belenson, S. M.; Kapur, K. C., An algorithm for solving multicriterion linear programming problems with examples, Operational Research Quarterly, 24, 1, 65-77 (1973) · Zbl 0261.90035
[3] Zeleny, M., A concept of compromise solutions and the method of the displaced ideal, Computers and Operations Research, 1, 479-496 (1974)
[4] Kim, G.; Park, C. S.; Yoon, K. P., Identifying investment opportunities for advanced manufacturing systems with comparative-integrated performance measurement, International Journal of Production Economics, 50, 23-33 (1997)
[5] Cheng, S.; Chan, C. W.; Huang, G. H., Using multiple criteria decision analysis for supporting decision of solid waste management, Journal of Environmental Science and Health, Part A, 37, 6, 975-990 (2002)
[6] Zanakis, S. H.; Solomon, A.; Wishart, N.; Dublish, S., Multi-attribute decision making: A simulation comparison of selection methods, European Journal of Operational Research, 107, 507-529 (1998) · Zbl 0943.90054
[7] Chen, M. F.; Tzeng, G. H., Combining gray relation and TOPSIS concepts for selecting an expatriate host country, Mathematical and Computer Modelling, 40, 1473-1490 (2004) · Zbl 1099.90549
[8] Janic, M., Multicriteria evaluation of high-speed rail, transrapid maglev, and air passenger transport in Europe, Transportation Planning and Technology, 26, 6, 491-512 (2003)
[9] Kwong, C. K.; Tam, S. M., Case-based reasoning approach to concurrent design of low power transformers, Journal of Materials Processing Technology, 128, 136-141 (2002)
[10] Milani, A. S.; Shanian, A.; Madoliat, R., The effect of normalization norms in multiple attribute decision making models: A case study in gear material selection, Structural Multidisciplinary Optimization, 29, 4, 312-318 (2005)
[11] Srdjevic, B.; Medeiros, Y. D.P.; Faria, A. S., An objective multi-criteria evaluation of water management scenarios, Water Resources Management, 18, 35-54 (2004)
[12] Yang, T.; Chou, P., Solving a multiresponse simulation-optimization problem with discrete variables using a multi-attribute decision-making method, Mathematics and Computers in Simulation, 68, 9-21 (2005) · Zbl 1108.93305
[13] Yoon, K.; Hwang, C. L., Manufacturing plant location analysis by multiple attribute decision making: Part I—single-plant strategy, International Journal of Production Research, 23, 345-359 (1985) · Zbl 0563.90037
[14] Lai, Y. J., TOPSIS for MODM, European Journal of Operational Research, 76, 486-500 (1994) · Zbl 0810.90078
[16] Shih, H. S.; Wang, C. H.; Lee, E. S., A multiattribute GDSS for aiding problem-solving, Mathematical and Computer Modelling, 39, 11-12, 1397-1412 (2004) · Zbl 1109.91334
[17] Saaty, T. L., The Analytic Hierarchy Process (1990), RWS Pub.: RWS Pub. Pittsburgh, PA · Zbl 1176.90315
[18] Saaty, T. L.; Ozdemir, M. S., Why the magic number seven plus or minus two, Mathematical and Computer Modelling, 38, 233-244 (2003) · Zbl 1106.91312
[19] Deng, H.; Yeh, C. H.; Willis, R. J., Inter-company comparison using modified TOPSIS with objective weights, Computers and Operations Research, 27, 963-973 (2000) · Zbl 0970.90038
[20] Chu, T. C., Facility location selection using fuzzy TOPSIS under group decision, International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems, 10, 6, 687-701 (2002) · Zbl 1065.90085
[21] Byun, H. S.; Lee, K. H., A decision support system for the selection of a rapid prototyping process using the modified TOPSIS method, International Journal of Advanced Manufacturing Technology, 26, 11-12, 1338-1347 (2005)
[22] Parkan, C.; Wu, M. L., Decision-making and performance measurement models with applications to robot selection, Computers and Industrial Engineering, 36, 503-523 (1999)
[23] Chen, C. T., Extensions of the TOPSIS for group decision-making under fuzzy environment, Fuzzy Sets and Systems, 114, 1, 1-9 (2000) · Zbl 0963.91030
[24] Parkan, C.; Wu, M. L., Process selection with multiple objective and subjective attributes, Production Planning and Control, 9, 2, 189-200 (1998)
[25] Hwang, C. L.; Lin, M. J., Group Decision Making under Multiple Criteria (1987), Springer-Verlag: Springer-Verlag Berlin
[26] Yoon, K. P.; Hwang, C. L., Multiple Attribute Decision Making: An Introduction (1995), Sage Pub.: Sage Pub. Thousand Oaks, CA
[27] Berberian, S. K., Fundamentals of Real Analysis (1999), Springer: Springer NY
[28] Steuer, R. E., Multiple Criteria Optimization: Theory, Computation, and Application (1986), John Wiley: John Wiley NY · Zbl 0663.90085
[29] Jones, D. F.; Mardle, S. J., A distance-metric methodology for the derivation of weights from a pairwise comparison matrix, Journal of the Operational Research Society, 55, 869-875 (2004) · Zbl 1060.90069
[30] Shipley, M. F.; Korvin, D. K.; Obit, R., A decision making model for multi-attribute problems incorporating uncertainty and bias measures, Computers and Operations Research, 18, 335-342 (1991)
[31] Olson, D. L., Comparison of weights in TOPSIS models, Mathematical and Computer Modelling, 40, 721-727 (2004) · Zbl 1066.90054
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.