The renewable energy transition of oil- and gas-producing countries has specific peculiarities due to the ambivalent position of these countries in the global energy market, both as producers and consumers of energy resources. This task becomes even more challenging when the share of oil and gas in the country’s GDP is very high. These circumstances pose serious challenges for long-term energy policy development and require compromising decisions to better align the existing and newly created energy policies of the country. The scale, scope, and pace of changes in the transition process must be well balanced, considering the increasing pressure of economic and environmental factors. The objective of this paper is to develop models that allow the selection of the most appropriate scenario for renewable energy transition in an oil- and gas-producing country. The distinguishing feature of the proposed model is that alternatives in the decision matrix are presented as scenarios, composed of a set of energy resources and the level of their use. Linguistic descriptions of the alternative scenarios are formalized in the form of fuzzy statements. For the problem solution, four different Multiple-Criteria Decision-Making (MCDM) methods were used: the fuzzy simple additive weighting (F-SAW) method, the distance-based fuzzy TOPSIS method (Technique of Order Preference Similarity to the Ideal Solution), the ratio-analysis-based fuzzy MOORA method (Multi-Objective Optimization Model Based on the Ratio Analysis), and the fuzzy multi-criteria optimization and compromise solution method VIKOR (Serbian: VIekriterijumsko Kompromisno Rangiranje). This approach is illustrated using the example of the energy sector of Azerbaijan. The recommended solution for the country involves increasing natural gas (NG) moderately, maintaining hydro, and increasing solar notably and wind moderately.