Chinese Journal of Computers   Full Text
Title	Uncertainty of Rough Sets in Different Knowledge Granularities
Authors	WANG Guo-Yin1),2) ZHANG Qing-Hua1),2)
Address	1)(School of Information Science &Technology, Southwest Jiaotong University, Chengdu 610031) 2)(Institute of Computer Science & Technology, Chongqing University of Posts and Telecommunications, Chongqing 400065)
Year	2008
Issue	No.9(1588—1598)
Abstract &   Background	Abstract Rougness, rough entropy, fuzziness, and fuzzy entropy are major methods for measuring the uncertainty of rough sets. In different knowledge granularity levels, a hierarchical knowledge space chain is proposed based on the attributes in information systems. Some regularities of the changing of rough entropy and fuzziness of a rough set with the knowledge granularity are found to be inconsistent with human cognition. A new method for measuring the fuzziness of rough sets is proposed based on information entropy. The fuzziness measured by the new method is monotonously decreasing with the refining of knowledge granularity in apporiximation spaces. It overcomes the problem of roughness and rough entropy. Finally, the relations of the changing of roughness and fuzziness are analyzed in different knowledge granularities. Keywords roughness; rough entropy; fuzziness; knowledge granularity; quotient space Background Uncertainty is an important property of uncertain set theories. Roughness, rough entropy, fuzziness, and fuzzy entropy are major methods for measuring the uncertainty of rough sets. However, we find that the regularities of the changing of rough entropy and fuzziness of a rough set with the knowledge granularity are inconsistent with human cognition. Granular computing (GrC) is a new method for simulating human thinking and solving complicated problems. It could be regarded as an umbrella covering the theories, methodologies and techniques of granularity. From the view of granular computing, the uncertainty of rough set should vary in different knowledge granularity levels. We find there is some limitation for roughness and rough entropy to measure the uncertainty of a rough set in different knowledge granularity levels. A new method for measuring the fuzziness of rough sets is proposed based on information entropy in this paper. The fuzziness measured by the new method is monotonously decreasing with the refining of knowledge granularity in apporiximation spaces. It overcomes the problem of roughness and rough entropy. In addition, the relations of the changing of roughness and fuzziness in different knowledge granularities are analyzed. This work is partially supported by the National Natural Science Foundation of China(No.60573068 and No.60773113), Science & Technology Research Program of the Municipal Education Committee of Chongqing of China (No.KJ060517) and Natural Science Foundation of Chongqing of China (No.2008BA2017).