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Based on special additivity of σ-entropy and proposition of monotone function, we study the structure of σ-entropy of fuzzy set. At first, we describe the structure of σ-entropy. Then, with this structure in place, we derive primary propositions of σ-entropy, and a conclusion of the entropy under lp-distance, that is, this entropy of fuzzy set has σ-additivity only if p equals 1.
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...
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