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Extenics is a new cross discipline to study rules and methods of solving contradictory problems in the real world. The basic concepts and theoretical frame of extenics are briefly introduced in this paper. Based on the merit of extenics, the extension evaluation method was applied to evaluate the brake materials according to a five-grade criterion established in this study. Considering the results computed by the original and simplified models, the similar conclusions were made: all four brake samples, marked A - D, were evaluated in the first grade based on the calculated dependence degrees, and sample B was judged as the best performing friction material with the highest dependence degree and the lowest wear rate.