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Vague软集理论被认为是一种新的处理不确定信息的数学工具,而模糊熵又是度量各种不确定信息的重要技术.文章基于Vague集思想和软集思想之间的联系,以及Vague集与软集现有理论,在Vague集模糊熵公理化定义的基础上,初步提出了Vague软集的模糊熵的公理化定义.同时给出了一种Vague软集的模糊熵的计算公式,并在此基础上证明了我们的模糊熵公式具有一些良好的数学性质.所得结果扩展了Vague软集理论的研究范围,并提出了该领域未来可研究的方向.
Vague soft set theory is considered as a new mathematical tool to deal with uncertain information, and fuzzy entropy is an important technique to measure various uncertain information.According to the connection between the ideas of Vague sets and soft sets, Based on the existing theory of set and soft set, the axiomatic definition of fuzzy entropy of Vague soft set is proposed based on the definition of fuzzy entropy axiomatization of Vague set.At the same time, a formula of fuzzy entropy of Vague soft set is given, On this basis, it is proved that our fuzzy entropy formula has some good mathematical properties.The results extend the research scope of Vague soft-set theory and propose the future research directions in this field.