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The technique of fast fault clearance for railway power transmission lines is an urgent and noticeable problem. According to the segmented structure characteristic of the lines, a novel fault location scheme based on the interval analysis and evidence theory is proposed. First, the interval model is addressed. The interval analysis is applied to deduce three interval algorithms, which implement interval location. Then, in terms of the characteristic of interval set, the difference matrix of deviation degree is used to represent quantitatively the degree of similarity between interval numbers, and construct an expression of basic probability assignment function. Finally, the evidence theory is introduced to combine the results of three interval algorithms and infer the fault segmented interval. The simulated results and practical application have effectively verified the accuracy and reliability of the proposed location scheme, which is suitable for all segmented structure lines.