Standard deviation method for determining the weights of group multiple attribute decision making under uncertain linguistic environment

The multi-attribute decision making problems are studied, in which the information about attribute weights is completely unknown and the attribute values take the form of uncertain linguistic variables. The concept of deviation degree between uncertain linguistic variables is defined. A formula of possibility degree for the comparison between uncertain linguistic variables is introduced and also some properties of the possible degree are also investigated. Based on the ideal that the attribute with a larger deviation value among alternatives should be evaluated a large weight, a method named standard deviation method is proposed to determine the weighting vector objectively. An illustrative example is examined using the proposed method. It is shown that the standard deviation method provides an effective way to determine the weights of the uncertain linguistic variables in group decision making.