犹豫模糊熵生成算法及在后勤补给基地选址评估中的应用

为了定量地刻画犹豫模糊信息的不确定性程度,将犹豫模糊元和区间值犹豫模糊元的熵推广成了犹豫模糊集和区间值犹豫模糊集的熵。首先给出了犹豫模糊集和区间值犹豫模糊集的熵与相似度的公理化定义,在此基础上提出了犹豫模糊集熵和相似度的一般公式,给出了犹豫模糊集的熵和相似度的生成算法。然后研究了犹豫模糊集的熵与相似度间的关系,提出了基于相似度的熵的一般公式。进一步把犹豫模糊集的熵与相似度的关系的有关结论及各自的一般公式和生成算法推广到区间值犹豫模糊集。最后给出了基于犹豫模糊集熵和相似度的后勤补给基地选址方案可靠性分析的数值例子。

Hesitant Fuzzy Entropy Generation Algorithms and Their Application in Location Evaluation of Logistics Supply Base

In order to quantitatively characterize the degree of uncertainty of hesitant fuzzy information, the entropy of hesitant fuzzy element and interval valued hesitant fuzzy element are generalized to the entropy of hesitant fuzzy sets and interval valued hesitant fuzzy sets. First of all, the axiomatic definitions of entropy and similarity measure of hesitant fuzzy sets and interval valued hesitant fuzzy sets are given. On this basis, a generalized formulae of entropy and similarity measure is proposed. The algorithms for generating entropy and similarity of hesitant fuzzy sets are given. Then, the relationship between the entropy and the similarity measure of the hesitant fuzzy sets is studied, and the generalized similarity based entropy formulae are proposed. Furthermore, the relevant conclusions of the relationship between the entropy and the similarity of the hesitant fuzzy set and their respective general formulas and generating algorithms are extended to that of interval valued hesitant fuzzy sets. Finally, a numerical example of the reliability analysis of the logistics supply base location scheme based on the entropy and similarity of hesitant fuzzy sets is given.