Abstract: The concept of generalized hesitant fuzzy soft set is proposed based on the generalized fuzzy soft set and hesitant fuzzy soft set in this paper, and the similarity measure of the generalized hesitant fuzzy soft sets is discussed. At first, the similarity measure formula of hesitant fuzzy set is constructed by using three kinds of inclusion degree of hesitant fuzzy sets. Then the axiomatic definition of similarity measures of the generalized hesitant fuzzy soft set is provided based on hesitant fuzzy set similarity measure, and similarity measure formula of the generalized hesitant fuzzy soft set is constructed. The similarity measure of generalized hesitant fuzzy soft sets with different parameter sets can be calculated by using these formulas. Finally, a decision method is constructed by using the similarity measurement of generalized hesitant fuzzy soft set, and the decision-making method is applied to the problems of environmental governance. It can be verified the feasibility and effectiveness of the proposed method.

Key words: generalized fuzzy soft set, hesitant fuzzy soft set, generalized hesitant fuzzy soft set, similarity measures, inclusion degrees

摘要： 在广义模糊软集和犹豫模糊软集的基础上给出广义犹豫模糊软集的概念，并研究广义犹豫模糊软集的相似度量。首先利用三种犹豫模糊集合的包含度，构造犹豫模糊集间的相似度量公式。然后在犹豫模糊集相似度基础上给出广义犹豫模糊软集相似度量的公理化定义，并构造广义犹豫模糊软集的相似度量公式，这些公式可以计算参数集不同时两个广义犹豫模糊软集间的相似度。最后利用广义犹豫模糊软集相似度量方法构造了一种决策方法，并将这个决策方法应用于环境治理问题中。通过实例验证了所提出方法的可行性和有效性。

关键词: 广义模糊软集, 犹豫模糊软集, 广义犹豫模糊软集, 相似度量, 包含度