Real-world data obtained from integrating heterogeneous data sources are often multi-valued, uncertain, imprecise, error-prone, outdated, and have different degrees of accuracy and correctness. It is critical to resolve data uncertainty and conflicts to present quality data that reflect actual world values. This task is called data fusion. In this paper, we deal with the problem of data fusion based on probabilistic entity linkage and uncertainty management in conflict data. Data fusion has been widely explored in the research community. However, concerns such as explicit uncertainty management and on-demand data fusion, which can cope with dynamic data sources, have not been studied well. This paper proposes a new probabilistic data fusion modeling approach that attempts to find true data values under conditions of uncertain or conflicted multi-valued attributes. These attributes are generated from the probabilistic linkage and merging alternatives of multi-corresponding entities. Consequently, the paper identifies and formulates several data fusion cases and sample spaces that require further conditional computation using our computational fusion method. The identification is established to fit with a real-world data fusion problem. In the real world, there is always the possibility of heterogeneous data sources, the integration of probabilistic entities, single or multiple truth values for certain attributes, and different combinations of attribute values as alternatives for each generated entity. We validate our probabilistic data fusion approach through mathematical representation based on three data sources with different reliability scores. The validity of the approach was assessed via implementation into our probabilistic integration system to show how it can manage and resolve different cases of data conflicts and inconsistencies. The outcome showed improved accuracy in identifying true values due to the association of constructive evidence.