Multi-attribute three-way decision making based on interval-valued intuitionistic fuzzy sets

In the interval-valued intuitionistic fuzzy environment, a new multi-attribute three-way decision-making model is proposed to address the problems that the relative loss function in the existing multi-attribute three-way decision-making model does not consider the degree of hesitancy, and the alternative conditional probabilities are given subjectively by the authors, which lacks objectivity. First, three types of ideal solutions are introduced, and the correlation coefficients between the evaluated values and ideal solutions are utilized to construct alternative relative loss functions. Second, the ELECTRE-I method is generalized to the interval-valued intuitionistic fuzzy environment to establish the outranking relation and a method for estimating the conditional probability of alternatives is given. Finally, the model is used to experimentally analyze examples to illustrate the effectiveness and rationality of the model.