The aim of this paper is to present a fusion approach of multi-granularity linguistic information for managing information assessed in di erent linguistic term sets (multi-granularity linguistic term sets) together with its application in a decision making problem with multiple information sources, assuming that the linguistic performance values given to the alternatives by the di erent sources are represented in linguistic term sets with di erent granularity and=or semantic. In this context, a decision process based on two steps is proposed with a view to obtaining the solution set of alternatives. First, the fusion of the multi-granularity linguistic performance values is carried out in order to obtain collective performance evaluations. In this step, on the one hand, the multi-granularity linguistic information is made uniform using a linguistic term set as the uniform representation base, the basic linguistic term set. On the other hand, the collective performance evaluations of the alternatives are obtained by means of an aggregation operator, being fuzzy sets on the basic linguistic term set. Second, the choice of the best alternative(s) from the collective performance evaluations is performed. To do that, a fuzzy preference relation is computed from the collective performance evaluations using a ranking method of pairs of fuzzy sets in the setting of Possibility Theory, applied to fuzzy sets on the basic linguistic term set. Then, a choice degree may be applied on the preference relation in order to rank the alternatives.