概率不确定语言熵及其多属性群决策

针对概率不确定语言集的多个不确定语言术语和其概率各不相同的特点，提出基于概率不确定语言熵的多属性决策方法。定义四种新的概率不确定语言熵：模糊熵、犹豫熵、不完全信息熵和总熵，以分别测量概率不确定语言集的模糊性、犹豫性、信息不完全性和整体不确定性。给出了四种熵测度的公理化定义和表达式，根据概率不确定语言集的四种熵，构建能够解决属性权重未知的多属性决策模型，并通过案例和对比分析验证了该模型的有效性和合理性。

Probabilistic Uncertain Linguistic Entropy and Its Application in Multi-attribute Group Decision Making

A multi-attribute decision-making method based on probabilistic uncertain linguistic entropy is proposed for the multiple uncertain linguistic terms of probabilistic uncertain linguistic term set and characteristics that their probabilistic is different. Firstly, four new probabilistic uncertain linguistic entropy measures are proposed, including the fuzzy entropy, the hesitant entropy, the lack of knowledge entropy and the total entropy to measure the fuzziness, hesitation, lack of knowledge and global uncertainty of probabilistic uncertain linguistic term set respectively. Secondly, the axiomatic definition and expressions of the four entropy measures are given. Finally, the multi-attribute decision-making model that can solve unknown attribute weights is constructed by the four entropy of probabilistic uncertain linguistic term set, and the validity and rationality of the model are verified by case and contrast analysis.