An extension of TOPSIS for group decision making.

*(English)*Zbl 1187.90166Summary: 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.

##### MSC:

90B50 | Management decision making, including multiple objectives |

##### Keywords:

TOPSIS; multi-attribute decision making; group decision support; preference aggregation; distance function; normalization##### Software:

MADM
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\textit{H.-S. Shih} et al., Math. Comput. Modelling 45, No. 7--8, 801--813 (2007; Zbl 1187.90166)

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