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模糊事件的概率就是它的平均隶属度。模糊事件的熵就是它的概率的负对数。结局为若干不相交模糊事件的随机试验的熵即是各结局的熵的平均值。信息是用熵的减量来度量的。 在模糊情况,总熵是由两个部分组成的。一部分是随机熵,另一部分是模糊熵;后者恰好等于由模糊性而损失的信息量。 模糊信息在生物学、医学、经济学、语言学与通信学中的应用是有广阔前景的。
The probability of fuzzy events is its average membership degree. The entropy of a fuzzy event is the negative logarithm of its probability. The entropy of a randomized trial whose outcome is a number of disjoint fuzzy events is the average of entropy of each outcome. Information is measured by entropy reduction. In the fuzzy case, the total entropy is composed of two parts. One is random entropy and the other is fuzzy entropy; the latter is exactly equal to the amount of information lost by fuzziness. The application of fuzzy information in biology, medicine, economics, linguistics and communication has broad prospects.