Meta-analyses offer interesting tools for combining the results of studies carried out by several authors on the strength of the observed effect of one variable on another, also called the effect size. The models proposed for the meta-analysis are within the statistical framework, which makes it possible to make hypotheses on the parametric probability laws related to the effect size variable. However, probability theory shows its limits for combining information from heterogeneous sources. In the absence of the assumption of homogeneity, the aggregation by a weighted average of the effect sizes, adopted in the meta-analyses to obtain the final effect size, does not seem to reflect the information provided by most sources. In this article, we propose a meta-analysis that takes advantage of possibility theory techniques to combine incomplete information from heterogeneous sources. The resulted possibility distribution allows to distinguish between plausible and less plausible values for the effect size of a treatment, for example, given trials performed by different authors. The illustration of the proposed possibilistic meta-analysis concerns the ”post-COVID-syndrome”. More precisely, the illustration focus on the prevalence of Fatigue symptom. The article shows that it is far from reality to consider the assumption of homogeneity for such data. Instead, group of coherent studies are identified using maximum coherent subsets. The results considering the two approaches are presented.