Goldman’s fuzzy reducts are subsets of attributes that allows for preserving the discernibility capacity of the whole set of attributes, in these subsets each attribute has an associated discernibility value, which can be interpreted as the capacity the correspeponing attribute has to discern objects of different class. Computing all Goldman’s fuzzy reducts is time-consuming, and few algorithms have been proposed in the literature. For these reasons, this paper introduces a new algorithm for computing all Goldman’s fuzzy reducts. The proposed algorithm traverses the search space following a new ordering and applies pruning properties, introduced in this paper, that help avoid exhaustively evaluating the reduct definition and discarding subsets. Additionally, we introduced a concept of density for simplified non-Boolean discernibility matrices that allows a density-based characterization of the algorithms’ performance. The proposed algorithm is evaluated and compared against state-of-the-art algorithms on synthetic and real decision systems. From our experiments, we determine the matrix type regarding density, where our algorithm performs the best.
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