Decomposed fuzzy sets (DFSs) are one of the latest extensions of intuitionistic fuzzy sets which are introduced to express vague and imprecise information to be used in multi-criteria decision-making. DFSs represent the human thinking structure in a multidirectional way, and they enable it through functional and dysfunctional judgments. However, DFSs cannot completely represent the entire human mindset as they are incapable of capturing reliability information, as it is in the other extensions, and this inability may cause wrong decisions to be given. To handle this problem, decomposed Z-fuzzy numbers, which are the integrated DFSs with reliability information provided by Z-fuzzy numbers, are introduced to model functional and dysfunctional judgments for taking the consistency of decision makers into account. Collecting judgments with both their fuzzy restrictions and fuzzy reliabilities from decision makers based on functional and dysfunctional questions provide more consistent and reliable judgments in the practice. Subsequently, a new decomposed Z-fuzzy linguistic scale and defuzzification formula are introduced to reach a final solution. Then, decomposed Z-fuzzy TOPSIS method is developed. Finally, we analyze the effect of the reliability parameter on the given decisions and present a comparative analysis with crisp TOPSIS method by an application of transfer center location selection for a private cargo company in Marmara Region of Turkey.