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Summary form only given. This paper presents a fuzzy distribution power flow (FDPF) for weakly meshed balanced and unbalanced distribution system. Most of the earlier work in this area is for radial distribution systems. In the proposed method a matrix similar to Jacobian inverse is directly evaluated, in an efficient manner. The method can handle simultaneous presence of several uncertainties in input variables such as network parameters, load model coefficients, load forecast and bus shunts. Results have been obtained for two test systems to assess the utility of the proposed method.