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A method for group decision-making based on determining weights of decision makers using TOPSIS. (English) Zbl 1217.91046

Summary: In general, weights of decision makers (DMs) play a very important role in multiple attribute group decision-making (MAGDM), how to measure the weights of DMs is an interesting research topic. This paper presents a new approach for determining weights of DMs in group decision environment based on an extended TOPSIS (technique for order preference by similarity to an ideal solution) method. We define the positive ideal solution as the average of group decision. The negative ideal solution includes two parts: left and right negative ideal solution, which are the minimum and maximum matrixes of group decision, respectively. We give an example to illustrate the developed approach. Finally, the advantages and disadvantages of this study are also compared.

MSC:

91B06 Decision theory
90B50 Management decision making, including multiple objectives

Software:

MADM
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Full Text: DOI

References:

[1] Saaty, T. L., The Analytic Hierarchy Process (1980), McGraw-Hill: McGraw-Hill New York · Zbl 1176.90315
[2] Hwang, C. L.; Yoon, K., Multiple Attribute Decision Making (1981), Springer-Verlag: Springer-Verlag Berlin · Zbl 0453.90002
[3] Zeleny, M., Multiple Criteria Decision Making (1982), McGraw-Hill: McGraw-Hill New York · Zbl 0588.90019
[4] Chen, S. J.J.; Hwang, C. L.; Beckmann, M. J.; Krelle, W., Fuzzy Multiple Attribute Decision Making: Methods and Applications (1992), Springer-Verlag New York, Inc.: Springer-Verlag New York, Inc. Secaucus, NJ, USA · Zbl 0768.90042
[5] Roy, B., Multicriteria Methodology for Decision Aiding (1996), Springer · Zbl 0893.90108
[6] Yager, R. R.; Kacprzyk, J., The Ordered Weighted Averaging Operators: Theory and Applications (1997), Kluwer Academic Publishers: Kluwer Academic Publishers Norwell, MA, USA · Zbl 0948.68532
[7] Belton, V.; Stewart, T. J., Multiple Criteria Decision Analysis: An Integrated Approach (2002), Springer
[8] Xu, Z. S., Uncertain Multiple Attribute Decision Making: Methods and Applications (2004), Qinghua university: Qinghua university China
[9] Yue, Z. L.; Jia, Y. Y.; Ye, G. D., An approach for multiple attribute group decision making based on intuitionistic fuzzy information, Int. J. Uncertainty, Fuzziness Knowledge Based Syst., 17, 3, 317-332 (2009) · Zbl 1185.91075
[10] French, J. R.P., A formal theory of social power, Psychol. Rev., 63, 3, 181-194 (1956)
[11] Theil, H., On the symmetry approach to the committee decision problem, Manage. Sci., 380-393 (1963)
[12] Keeney, R. L.; Kirkwood, C. W., Group decision making using cardinal social welfare functions, Manage. Sci., 22, 4, 430-437 (1975) · Zbl 0339.90002
[13] Keeney, R. L., A group preference axiomatization with cardinal utility, Manage. Sci., 23, 2, 140-145 (1976) · Zbl 0351.90004
[14] Bodily, S. E., A delegation process for combining individual utility functions, Manage. Sci., 25, 10, 1035-1041 (1979) · Zbl 0465.90004
[15] Xu, Z., Group decision making based on multiple types of linguistic preference relations, Inform. Sci., 178, 2, 452-467 (2008) · Zbl 1130.91321
[16] Mirkin, B. G.; Fishburn, P. C., Group Choice (1979), Halsted Press · Zbl 0406.92023
[17] Ben Khèlifa, S.; Martel, J.-M., Deux propositions d’aide multicritère à la décision de groupe, (Abdelaziz, Ben; et Mellouli, Haouari, Optimisation et Décision (2000), Centre de Publication Universitaire: Centre de Publication Universitaire Tunis), 213-228
[18] Van den Honert, R. C., Decisional power in group decision making: a note on the allocation of group members’ weights in the multiplicative AHP and SMART, Group Decis. Negot., 10, 3, 275-286 (2001)
[19] Jabeur, K.; Martel, J. M., Quantification de l’importance relative des membres d’un groupe en vue d’établir un préordre collectif, Inform. Syst. Oper. Res., 40, 3, 181-198 (2002) · Zbl 07677763
[20] Brock, H. W., The problem of “utility weights” in group preference aggregation, Oper. Res., 28, 1, 176-187 (1980) · Zbl 0425.90007
[21] Ramanathan, R.; Ganesh, L. S., Group preference aggregation methods employed in AHP: An evaluation and an intrinsic process for deriving members’ weightages, Eur. J. Oper. Res., 79, 2, 249-265 (1994) · Zbl 0815.90003
[22] Chen, X.; Fan, Z. P., Study on assessment level of experts based on difference preference information, Syst. Eng. Theory Pract., 27, 2, 27-35 (2007)
[23] Yue, Z. L., An extended TOPSIS for determining weights of decision makers with interval numbers, Knowledge Based Syst., 24, 1, 146-153 (2011)
[24] Yoon, K.; Hwang, C. L., Multiple Attribute Decision Making: An Introduction (1995), Sage Publications, Inc
[25] Roghanian, E.; Rahimi, J.; Ansari, A., Comparison of first aggregation and last aggregation in fuzzy group TOPSIS, Appl. Math. Model., 34, 12, 3754-3766 (2010) · Zbl 1201.91037
[26] Kao, C., Weight determination for consistently ranking alternatives in multiple criteria decision analysis, Appl. Math. Model., 34, 7, 1779-1787 (2010) · Zbl 1193.91043
[27] Belenson, S. M.; Kapur, K. C., An algorithm for solving multicriterion linear programming problems with examples, Oper. Res. Quart., 24, 1, 65-77 (1973) · Zbl 0261.90035
[28] Zeleny, M., A concept of compromise solutions and the method of the displaced ideal, Comput. Oper. Res., 1, 4, 479-496 (1974)
[29] Sayadi, M. K.; Heydari, M.; Shahanaghi, K., Extension of VIKOR method for decision making problem with interval numbers, Appl. Math. Model., 33, 5, 2257-2262 (2009) · Zbl 1185.91071
[30] Yang, T.; Chou, P., Solving a multiresponse simulation-optimization problem with discrete variables using a multiple-attribute decision-making method, Math. Comput. Simul., 68, 1, 9-21 (2005) · Zbl 1108.93305
[31] Lin, Y. H.; Lee, P. C.; Chang, T. P.; Ting, H. I., Multi-attribute group decision making model under the condition of uncertain information, Autom. Constr., 17, 6, 792-797 (2008)
[32] Jahanshahloo, G. R.; Lotfi, F. H.; Izadikhah, M., An algorithmic method to extend TOPSIS for decision-making problems with interval data, Appl. Math. Comput., 175, 2, 1375-1384 (2006) · Zbl 1131.90386
[33] Chamodrakas, I.; Leftheriotis, I.; Martakos, D., In-depth analysis and simulation study of an innovative fuzzy approach for ranking alternatives in multiple attribute decision making problems based on TOPSIS, Appl. Soft Comput., 11, 1, 900-907 (2011)
[34] Shih, H. S.; Shyur, H. J.; Lee, E. S., An extension of TOPSIS for group decision making, Math. Comput. Model., 45, 7-8, 801-813 (2007) · Zbl 1187.90166
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