Dominance-based rough set approach to incomplete fuzzy information system

Although many extended rough set models have been successfully applied into the incomplete information system, most of them do not take the incomplete information system with initial fuzzy data into account. This paper thus presents a general framework for the study of dominance-based rough set model in the incomplete fuzzy information systems. First, the traditional dominance relation is expanded in the incomplete fuzzy information system. We then present the dominance-based rough approximations by the rough fuzzy technique. Finally, we propose two types of knowledge reductions, relative lower and upper approximate reducts, which can be used to induce simplified decision rules from the incomplete fuzzy decision table. We also present the judgement theorems and discernibility functions which describe how relative lower and upper approximate reducts can be calculated. We employ some numerical examples in this paper to substantiate the conceptual arguments.