Green supplier selection is a vital task for the modern tourism industry, and this necessitates the search for optimal and sustainable solutions to the problem. The complexity and heterogeneity of the tourism sector stipulate the usage of imperfect information in decision-making. For the formalization of such information, the approach based on Z-numbers is more acceptable and well recommended. The study presents a solution to the problem of selecting a green supplier for hotels based on the rank reversal-free multi-criteria decision-making approach. After specifying a decision matrix based on Z-numbers and a preference matrix, based on direct calculations with Z-number, the issues of determining the criteria weights, normalizing the decision matrix, and calculating the components of the vector of alternatives are sequentially solved. To determine the best alternative, the distance between the Z-numbers expressing the given alternatives and the ideal solution is calculated. The rank reversal-free approach use allows us to keep the order of the previous alternatives when adding a new alternative and evaluate new suppliers more relevantly. This is especially important for such a complex and highly competitive dynamic system as tourism. The results obtained show that the applied approaches can be successfully used not only in tourism but also in other areas of activity.