参数化犹豫模糊熵及其应用

犹豫模糊熵是刻画犹豫模糊集不确定程度的重要工具。针对现有犹豫模糊熵的一些不足，首先基于犹豫模糊集提出犹豫模糊熵的公理化定义，并构造出参数化犹豫模糊熵；其次，通过一些具体数值算例，将新提出的参数化犹豫模糊熵与现有犹豫模糊熵进行对比分析，结果显示所研究的熵能够更加灵活有效地描述信息的未知程度；然后，探究了参数化犹豫模糊熵在多属性决策问题中的应用，使用该熵来确定属性的权重，并借助逼近于理想解排序法（TOPSIS）以及分数函数，提出了一种解决最优方案选取问题的方法；最后，通过具体实例，验证了参数化犹豫模糊熵与所给决策方法具有一定的实用性和可行性。

Parametric hesitant fuzzy entropy and its application

Hesitant fuzzy entropy is an important tool for depicting the uncertainty degree of hesitant fuzzy set. In order to solve the shortcomings of the existing hesitant fuzzy entropies, the axiomatic definition of hesitant fuzzy entropy is proposed based on hesitant fuzzy set, and the parametric hesitant fuzzy entropy is constructed. Secondly, some numerical examples are given to compare the new parametric hesitant fuzzy entropy with the existing fuzzy entropies. The results show that the proposed entropy can describe the uncertainty degree of information more flexibly and effectively. Then, the application of parametric hesitation fuzzy entropy in multi-attribute decision-making problem is explored. The proposed entropy is used to determine the weight of the attribute. Technique for Order Preference by Similarity to an Ideal Solution (TOPSIS) and fractional function are adopted to present a method to solve the optimal scheme selection problem. Finally, an example is used to verify that the parametric hesitation fuzzy entropy and the proposed decision method has some practicability and feasibility.