Abstract: The loss function in decision-theoretic rough set theory is generally a single-valued function．Considering the “uncertainty” character in practical decision-making,we introduced a fuzzy-number based loss function to deal with a more general decision-making problem under uncertainty．The fuzzy distributions of the decision thresholds α,β were calculated through series of fuzzy operations,and the corresponding decision rules were given．A method for getting more compact supremum and infimum of the thresholds α,β was also presented．An example of oil investment was given to illuminate the proposed model in applications.

Key words: Decision-theoretic rough set theory,Probabilistic rough set theory,Bayesian decision procedure,Fuzzy number