区间值直觉模糊集（IVIFS）是一种有效的不确定性建模工具，受到了广泛关注。在应用IVIFS解决多属性决策（MADM）问题等实际问题时，如何测量两个区间值直觉模糊值（IVIFV）之间的距离是一个基本问题。在本文中，提出了一种新的 IVIFS 距离，称为间隔值直觉模糊 Jenson-Shannon (IVIFJS) 散度，它可以衡量 IVIFS 之间的差异或相异性。首先，我们提出了一种新的IVIFV评估评分函数，该评分函数考虑了会员和非会员的权重，比IVIFV现有的其他评分函数更灵活。然后，我们发现评估分数函数被包含在一个固定的区间内，表示为最大可能范围。此外，我们发现评估分数函数可以近似地认为在其最大范围内具有高斯分布。基于此，我们通过从离散 Jenson-Shannon (JS) 散度扩展，提出了一种新的 IVIFS 散度度量算子，称为区间值直觉模糊 Jenson-Shannon (IVIFJS) 散度。JS 散度的一些有用的数学性质，包括有界性、对称性和三角不等式，在所提出的 IVIFJS 散度中得到保持。接下来，我们基于所提出的散度算子设计了一种新的 MADM 方法。此外，通过与其他现有的 MADM 方法进行比较，评估了一些数值示例以说明所提出方法的适用性和合理性。然后，通过对数值例子的敏感性分析，验证了所提出的 MADM 方法的鲁棒性和稳定性。最后，将提出的MADM方法应用于医学诊断和网络系统选择的应用，验证了该方法的实用性。
Interval-Valued Intuitionistic Fuzzy Set (IVIFS) is an effective tool to model uncertainty, and has received much attention. When applying IVIFS to solve real problems such as Multi-Attribute Decision Making (MADM) problem, how to measure the distance between two Interval-Valued Intuitionistic Fuzzy Values (IVIFVs) is an essential problem. In this paper, a novel distance of IVIFS called Interval-Valued Intuitionistic Fuzzy Jenson-Shannon (IVIFJS) divergence is proposed, which can measure the difference or dissimilarity between IVIFSs. First, we propose a new Evaluation Score Function of the IVIFV, the score function considering the weight of membership and non-membership, which is more flexible than other existing score functions of IVIFV. Then, we find that the Evaluation Score Function is enclosed in a fixed interval, denoted as the largest possible range. Additionally, we find that the Evaluation Score Function can be approximately regarded to have Gaussian distribution over its largest range. Based on this, we propose a novel divergence measure operator for IVIFS named Interval-valued Intuitionistic Fuzzy Jenson-Shannon (IVIFJS) divergence by extending from discrete Jenson-Shannon (JS) divergence. Some useful mathematical properties of JS divergence, including boundness, symmetric and triangular inequality, are maintained in the proposed IVIFJS divergence. Next, we design a novel MADM method based on the proposed divergence operator. Further, some numerical examples are evaluated to illustrate the applicability and plausibility of the proposed method by comparing with other existing MADM methods. Then, the robustness and stability of the proposed MADM method are verified through sensitivity analysis on numerical examples. Finally, the proposed MADM method is applied in the applications of medical diagnosis and network system selection to verify the practicability of the proposed method.
