A method based on interval-valued fuzzy soft set for multi-attribute group decision-making problems under uncertain environment

In this paper, we develop a new method for multiple attributes group decision-making problems under uncertain environment, in which the information about attribute weights is incompletely known or completely unknown, and each maker’s decision information is expressed by an interval-valued fuzzy soft set. Moreover, this paper takes account of the decision makers’ attitude toward risk. In order to get the weight vector of the attributes, we construct the score matrix of the final fuzzy soft set. From the score matrix and the given attribute weights information, we establish an optimization model to determine the weights of attributes. For the special situations where the information about attribute weights is completely unknown, we establish another optimization model. By solving this model, we get a simple and exact formula, which can be used to determine the attribute weights. According to these models, a method based on interval-valued fuzzy soft set, which considers the decision makers’ risk attitude under uncertain environment, is given to rank the alternatives. Finally, a numerical example is used to illustrate the applicability of the proposed approach.