A novel three-way decision method for interval-valued hesitant fuzzy environment

In this paper, a novel way to solve the multi-attribute decision-making issues under the interval-valued hesitant fuzzy environment (IVHF-MADM) with three-way decision (3WD) theory is explored. Firstly, the RLF under the interval-valued hesitant fuzzy (IVHF) environment is defined. Then, in view of the practical significance of the loss function, the relationship between the loss function and the evaluation value is established. At the same time, considering that the IVHF-MADM has multiple attributes and multiple evaluation values, an aggregated loss function via the interval-valued hesitant fuzzy weight average operator to reflect the overall loss of the alternative is provided. And the mixed information table (IVHF-MADMRLF) based on the overall loss function is established. Secondly, based on an outranking function and a distance from the positive ideal PIS, we define an estimation on the conditional probability method. Finally, the choice of line site, which is closely related to the cost of building the entire project, traffic safety, and economic development along the line, is discussed in more details using a case study of a traffic expressway. Moreover, we propose the parameters analysis approach to the test in terms of its viability and efficiency.