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Journal of Information Science
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Novel fuzzy information proximity measures

Shi-Fei Ding

College of Computer Science and Technology, China University of Mining and Technology, Xuzhou, China, dingsf{at}cumt.edu.cn

Shi-Xiong Xia

College of Computer Science and Technology, China University of Mining and Technology, Xuzhou, China

Feng-Xiang Jin

College of Geoinformation Science and Engineering. Shandong University of Science and Technology, Qingdao, China

Zhong-Zhi Shi

Key Laboratory of Intelligent Information Processing, Institute of Computing Technology, Chinese Academy of Sciences, Beijing, China

As a measure of information shared between two fuzzy pattern vectors, the fuzzy information proximity measure (FIPM) plays an important part in fuzzy pattern recognition, fuzzy clustering analysis and fuzzy approximate reasoning. In this paper, two novel FIPMs are set up. Firstly, an axiom theory about the FIPM is given, and different expressions of the FIPM are discussed. A new FIPM is then proposed based on the axiom theory of the FIPM and the concept of fuzzy subsethood function. Two concepts based on the idea of Shannon information entropy, fuzzy joint entropy (FJE) and fuzzy conditional entropy (FCE), are proposed and the basic properties of FJE and FCE are given and proved. Finally, classical similarity measures such as dissimilarity measure (DM) and similarity measure (SM) are studied, and two new measures, fuzzy absolute information measure (FAIM) and fuzzy relative information measure (FRIM), are set up, which can be used as measures of the proximity between fuzzy sets A and B.

Key Words: Fuzzy information proximity measure (FIPM) • fuzzy nearness degree • fuzzy joint entropy (FJE) • fuzzy conditional entropy (FCE) • fuzzy absolute information measure (FAIM) • fuzzy relative information measure (FRIM)

This version was published on December 1, 2007

Journal of Information Science, Vol. 33, No. 6, 678-685 (2007)
DOI: 10.1177/0165551507076332
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