In this paper, a novel approach and framework based on interval-dependent degree and probability distribution for multi-criteria decision-making problems with multi-valued neutrosophic sets (MVNSs) is proposed. First, a simplified dependent function and distribution function are given and integrated into a concise formula, which is called the interval-dependent function and contains interval computing and probability distribution information in an interval. Then a transformation operator is defined and it is shown how to convert MVNSs into an interval set. Subsequently, the interval-dependent function with the probability distribution of MVNSs is deduced. Finally, an example and comparative analysis are provided to verify the feasibility and effectiveness of the proposed method. In addition, uncertainty analysis, which reflects the dynamic change of the ranking result with decision-makers’ preferences, is performed by setting different distribution functions, which increases the reliability and accuracy of the proposed method.

中文翻译：

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具有概率分布的多值中智集多准则决策问题的新稳定方法

在本文中，提出了一种基于区间依赖度和概率分布的多值中智集（MVNS）多准则决策问题的新方法和框架。首先，给出一个简化的依赖函数和分布函数，并整合成一个简洁的公式，称为区间依赖函数，包含区间计算和区间内的概率分布信息。然后定义了一个转换算子，并展示了如何将 MVNS 转换为一个区间集。随后，推导了具有MVNS概率分布的区间依赖函数。最后通过实例和对比分析验证了所提方法的可行性和有效性。此外，不确定性分析，