犹豫直觉模糊集的知识测度及其应用

犹豫直觉模糊集集成了直觉模糊集与犹豫模糊集的优点，能够更好地处理决策者偏好不一致时的不确定性问题。通过考虑决策者提供信息的犹豫性与模糊性，给出了犹豫直觉模糊集上知识测度的公理化定义，并且构建出犹豫直觉模糊集上一类含参知识测度，这类知识测度可以有效地刻画犹豫直觉模糊集所包含的信息量和决策者的态度特征。接下来，基于对该类知识测度中的参数进行讨论，得到一系列代表决策者不同态度特征的知识测度，进一步验证了知识测度与决策者态度系数的变化成正比。最后，基于犹豫直觉模糊集的知识测度提出多属性群决策方法，并将此方法应用于某互联网公司的空调安装公司选择的案例中，证明了所提出的知识测度具有有效性与实用性。

Knowledge measure of hesitant intuitionistic fuzzy set and its applications

The hesitant intuitionistic fuzzy set integrates the advantages of the intuitionistic fuzzy set and the hesitant fuzzy set, and can deal with the uncertainty problems with inconsistent preferences of decision makers perfectly. By considering the hesitancy and fuzziness of information provided by decision makers, the axiomatic definition of the knowledge measure on the hesitant intuitionistic fuzzy set is proposed. Besides, a class of parametric knowledge measure model that comply the axiom is developed, which can not only effectively depict the information in the hesitant intuitionistic fuzzy set, but also indicate the attitude characteristics of decision makers. Next, based on the discussion of the parameters in the knowledge measure, an amount of knowledge measures representing different attitude characteristics of decision makers are obtained. Furthermore, it is verified that the knowledge measure is proportional to the change of the attitude coefficient. Finally, a multiple attribute group decision making method based on the constructed knowledge measure of the hesitant intuitionistic fuzzy set is proposed. Meanwhile, a practical application, i.e., air conditioning installation company selection of an Internet company, demonstrates the effectiveness and practicability of the developed measure.