The maximizing deviation method for group multiple attribute decision making under linguistic environment

The aim of this paper is to put forward a method for multi-attribute decision making problems with linguistic information, in which the preference values take the form of linguistic variables. An aggregating operator named linguistic weighted arithmetic averaging (LWAA) operator is introduced to aggregate the given decision information to get the overall preference value of each alternative. Some properties of the LWAA operator are also investigated. Based on the idea that the attribute with a larger deviation value among alternatives should be evaluated a larger weight, a method to determine the optimal weighting vector of LWAA operator is developed under the assumption that attribute weights are completely unknown. The based approach is extended to the situation where partially weight information can be obtained by solving a constrained non-linear optimization problem. Then a procedure to group multiple attribute decision making is provided under linguistic environment. Finally, an example of risk investment problem is given to verify the proposed approach; a comparative study to fuzzy ordered weighted averaging (F-OWA) operator methods is also demonstrated.