The conversion formula between sigma-entropy and sigma-similarity measure of fuzzy sets

Liu has gotten the conversion formula between /spl sigma/-entropy and /spl sigma/-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.