Abstract: In multi-attribute group decision making, the heterogeneity of entities causes a lot difficulties for the interpretable evidence fusion reasoning process, thus a novel heterogeneous evidential chains based fusion reasoning(Hefur) method is proposed for multi-attribute group decision making. Based on the theory of evidential reasoning, the concept of evidential chain association is introduced to obtain the nearest neighbor set of distinct evidences from the data matrix of multiple decision tables. Similarity matrices are derived from data tables, and positive semi-definite matrix quadratic optimization model is built to share, sharing the experience knowledge of the group decision-making experts. Using the Dempster's quadrature rule, the rationality of the belief integrating is verified in the interpretable reasoning process with heterogeneous entities, and the combined belief is obtained from nearest neighbor evidences for each data table using the evidence fusion rules. Moreover, the validity is verified for dealing with the harmonic information inconsistence of the multi-heterogeneous data sources. Numerical experiments on the heart disease diagnosis with entity heterogeneity illustrate the feasibility and rationality of the proposed method.