Abstract
Probabilistic rough set model and graded rough set model are used to measure relative quantitative information and absolute quantitative information between equivalence classes and basic concepts, respectively. Since fuzzy concepts are more common in real life than classical concepts, how to use relative and absolute quantitative information to determine fuzzy concepts is a extremely important research topic. In this study, we propose a double-quantitative decision theory rough fuzzy set frame based on the fusion of decision theory rough set and graded rough set, and the framework mainly studies the fuzzy concepts in multigranulation approximation spaces. Three pairs of double-quantitative multigranulation decision theory rough fuzzy set models are established. Some basic characteristics of these models are discussed. The decision rules including relative and absolute quantitative information are studied. The intrinsic relationship between the double-quantitative decision theory rough fuzzy set and the multigranulation rough set is analyzed. Finally, an illustrative case of medical diagnosis is conducted to explain and evaluate the dual quantitative decision theory approach.
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