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First of all, a new distance incorporating decision attributes is defined, and then a relation between fuzzy evidence theory and fuzzy <jats:inline-formula><jats:alternatives><jats:tex-math>$$\\beta $$<\/jats:tex-math><mml:math xmlns:mml=\"http:\/\/www.w3.org\/1998\/Math\/MathML\">\n                  <mml:mi>\u03b2<\/mml:mi>\n                <\/mml:math><\/jats:alternatives><\/jats:inline-formula> covering with an anti-noise mechanism is established. In this framework, two robust feature selection algorithms for hybrid data are proposed based on fuzzy belief and fuzzy plausibility. Experiments on 10 data sets of various types show that compared with the other 6 state-of-the-art algorithms, the proposed algorithms improve the anti-noise ability by at least 6% with higher average classification accuracy. 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