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Decision-theoretic rough set approach for fuzzy decisions based on fuzzy probability measure and decision making

Most existing studies on decision-theoretic rough set approach focus on crisp decisions. However, in many cases, we need to handle fuzzy concepts. This paper investigates decision-theoretic rough set approach for fuzzy decisions. By introducing fuzzy operators, we extend the traditional decision-theoretic rough set approach with crisp decisions to fuzzy concepts. Decision-theoretic rough set approach with fuzzy concepts is investigated based on fuzzy probabilistic approxi- mation space. Bayesian decision procedure based on fuzzy probabilistic approximation space with fuzzy concepts and fuzzy probabilistic decision systems with fuzzy or continuous decision attributes are studied. The application of the proposed approach in decision making is also illustrated by an example. This study may expand the applications of decision-theoretic rough set model.