Double-quantitative rough fuzzy set based decisions: A logical operations method

As two important expanded quantification rough set models, the probabilistic rough set (PRS) model and the graded rough set (GRS) model are used to measure relative quantitative information and absolute quantitative information between the equivalence classes and a basic concept, respectively. The decision-theoretic rough set (DTRS) model is a special case of PRS model which mainly utilizes the conditional probability to express relative quantification. Since the fuzzy concept is more general than classical concept in real life, how to make decision for a fuzzy concept using relative and absolute quantitative information is becoming a hot topic. In this paper, a couple of double-quantitative decision-theoretic rough fuzzy set (Dq-DTRFS) models based on logical conjunction and logical disjunction operation are proposed. Furthermore, we discuss decision rules and the inner relationship between these two models. Then, an experiment in the medical diagnosis is studied to support the theories. Finally, to apply our methods to solve a pattern recognition problem in big data, experiments on data sets downloaded from UCI are conducted to test the proposed models. In addition, we also offer a comparative analysis using two non-rough set based methods. From the results obtained, one finds that the proposed method is efficient for dealing with practical issues.