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Journal of Information Science and Engineering, Vol. 21 No. 6, pp. 1227-1245 (November 2005)

Measuring Fuzziness in Rough Sets*

Hsuan-Shih Lee
Department of Shipping and Transportation Management
National Taiwan Ocean University
Keelung, 202 Taiwan
E-mail: hslee@axp1.stm.ntou.edu.tw

This paper presents a new fuzziness measure for rough sets. Fuzziness measures for rough sets may be employed to describe the inconsistency of a decision table. The definition of the fuzziness of a rough set proposed by Chakrabarty et al. has two drawbacks. The first is that the fuzziness of a rough set may not be unique. The second is that the fuzziness of a rough set with a large boundary may be very small. The aim of this paper is to present a new definition of the fuzziness measure for rough sets. The proposed fuzziness measure overcomes the drawbacks of the measure proposed by Chakrabarty et al. That is, with the new measure, each rough set has a unique fuzziness, and the fuzziness is in proportional to the size of the boundary. Moreover, the fuzziness of a rough set can be easily computed with the boundary of the rough set.

Keywords: fuzziness measure, fuzziness of a rough set, fuzzy sets, rough sets, roughness of a fuzzy set

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Received August 21, 2003; revised June 30, 2004; accepted September 23, 2004.
Communicated by Chin-Teng Lin.
* This research work was partially supported by the National Science Council of the Republic of China under grant No. NSC 92-2416-H-019-004.