In order to use three-way decision (TWD) to solve multiple attribute decision making (MADM) problems, in this article, a new TWD model with intuitionistic fuzzy numbers (IFNs) is proposed. First of all, we define the relative loss functions to demonstrate some features of loss functions in TWDs, which is the basis for future research. Then, based on the correlation between the loss functions and the IFNs, we get the relative loss functions based on IFNs. At the same time, the classification rules of the TWDs are discussed from different viewpoints, including the thresholds and their properties. Aiming at MADM problems with unreasonable values, a new integrated method of relative loss functions is established to obtain a fairer loss integration result of alternatives. In addition, considering that there are no decision attributes and only condition attributes in MADM, we use grey relational degree to calculate the condition probability. In the end, a novel TWD model is proposed to solve MADM problems with IFNs, and a practical example on selecting suppliers is used to demonstrate its effectiveness and practicability.