Title :
The conversion formula between sigma-entropy and sigma-similarity measure of fuzzy sets
Author :
Tong, Xiao-jun ; Zhang, She-Min ; Li, Zhi-Jun ; Xu, Xiao-Zeng
Author_Institution :
Dept. of Control Sci. & Eng., Huazhong Univ. of Sci. & Technol., Wuhan, China
Abstract :
Liu has gotten the conversion formula between σ-entropy and σ-similarity measure of fuzzy sets. But this formula is so correlative with the fuzziest set that the proof of the conversion formula is special complicated. We renewedly prove that the function defined by the conversion formula is a similarity measure of fuzzy sets depending on the simplified conversion formula. Our proof is completely divorced from Liu´s original eight fuzzy sets, which was constructed from fuzziest sets. And a laconic proof of mutual conversion formula is given.
Keywords :
entropy; fuzzy set theory; theorem proving; fuzzy set; laconic proof; mutual conversion formula; sigma-entropy measure; sigma-similarity measure; similarity measure; Cybernetics; Entropy; Finance; Forward contracts; Fuzzy sets; Machine learning; Mathematics; Pattern recognition; Physics; σ-entropy; σ-similarity measure; Fuzzy set;
Conference_Titel :
Machine Learning and Cybernetics, 2005. Proceedings of 2005 International Conference on
Conference_Location :
Guangzhou, China
Print_ISBN :
0-7803-9091-1
DOI :
10.1109/ICMLC.2005.1527396
