In this study, a two-phase methodology for resource allocation problems under a fuzzy environment is proposed. In the first phase, the imprecise Shannon's entropy method and the acceptability index are suggested, for the first time in the literature, to select input and output variables to be used in the data envelopment analysis (DEA) application. In the second step, an interval inverse DEA model is executed for resource allocation in a short run. In an effort to exemplify the practicality of the proposed fuzzy model, a real case application has been conducted involving 16 cement firms listed in Borsa Istanbul. The results of the case application indicated that the proposed hybrid model is a viable procedure to handle input-output selection and resource allocation problems under fuzzy conditions. The presented methodology can also lend itself to different applications such as multi-criteria decision-making problems.