An extension of TOPSIS to MAGDM with uncertain linguistic information

Technique for order performance by similarity to ideal solution (TOPSIS) is a practical and useful technique for ranking and selection of a number of alternatives through distance measures. It is extended to group decision making problems with uncertain linguistic information in this paper: The operational laws of uncertain linguistic variables and the distance of n-dimensional uncertain linguistic variables are defined. A closeness coefficient is defined to determine the ranking order of all alternatives by calculating the distances to both the positive ideal solution and the negative ideal solution simultaneously. The numerical example has shown the application of the proposed method in multi-attribute group decision making (MAGDM) problems with uncertain linguistic information.