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Fuzzy probabilistic approximation spaces and their information measures

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4 Author(s)
Qinghua Hu ; Harbin Inst. of Technol., China ; D. Yu ; Zongxia Xie ; Jinfu Liu

Rough set theory has proven to be an efficient tool for modeling and reasoning with uncertainty information. By introducing probability into fuzzy approximation space, a theory about fuzzy probabilistic approximation spaces is proposed in this paper, which combines three types of uncertainty: probability, fuzziness, and roughness into a rough set model. We introduce Shannon's entropy to measure information quantity implied in a Pawlak's approximation space, and then present a novel representation of Shannon's entropy with a relation matrix. Based on the modified formulas, some generalizations of the entropy are proposed to calculate the information in a fuzzy approximation space and a fuzzy probabilistic approximation space, respectively. As a result, uniform representations of approximation spaces and their information measures are formed with this work

Published in:

IEEE Transactions on Fuzzy Systems  (Volume:14 ,  Issue: 2 )