Abstract:

The existing entropy of the extended hesitant fuzzy linguistic term set cannot distinguish the uncertainty of the extended hesitant fuzzy linguistic term set which is equal to the complement set, and there is relatively little consideration of hesitation in the hesitant fuzzy linguistic information, which does not fully reflect the uncertainty of the hesitant fuzzy linguistic information. This paper improves the definition of the entropy for extended hesitant fuzzy linguistic term sets, and describes the uncertainty of the extended hesitant fuzzy linguistic term set from the aspects of fuzziness and hesitation. The fuzzy entropy and hesitant entropy of the extended hesitant fuzzy linguistic term set are defined respectively. The general formula and generating algorithm of fuzzy entropy and hesitant entropy are given. Then the total entropy of the extended hesitant fuzzy linguistic term set is defined, and the general formula for total entropy is proposed. Finally, a multi-attribute decision-making example of the promotion optimization evaluation of college professors based on the entropy of the hesitant fuzzy linguistic term set is given, and the feasibility and effectiveness of the decision-making method are illustrated through comparative analysis.

Key words: hesitant fuzzy linguistic term set, fuzzy entropy, hesitant entropy, total entropy, multi-attribute decision making

摘要：

由于现有的扩展犹豫模糊语言术语集的熵无法区分与补集相等的扩展犹豫模糊语言术语集的不确定性，并且对犹豫模糊语言信息中的犹豫性考虑得相对较少，无法全面地反映犹豫模糊语言信息的不确定性。改进了扩展犹豫模糊语言术语集的熵的定义，从模糊性和犹豫性两方面刻画了扩展犹豫模糊语言术语集的不确定性，分别定义了扩展犹豫模糊语言术语集的模糊熵和犹豫熵，给出了模糊熵和犹豫熵的一般公式与生成算法。定义了一个扩展犹豫模糊语言术语集的总熵，给出了总熵的一般公式。最后给出了一个基于犹豫模糊语言熵的高校教授晋升优选评估的多属性决策算例，通过比较分析说明了决策方法的可行性与有效性。

关键词: 犹豫模糊语言术语集, 模糊熵, 犹豫熵, 总熵, 多属性决策