We propose a method to approximate Intuitionistic Fuzzy Sets (IFSs) with Shadowed Sets that could be used, in decision making or similar tasks, when the full information about membership values is not necessary, is difficult to process or to interpret. Our approach is based on an information‐theoretic perspective and aims at preserving the uncertainty, represented through an entropy measure, in the original IFS by minimizing the difference between the entropy in the input IFS and the output Shadowed Set. We propose three different efficient optimization algorithms that retain Fuzziness, Lack of Knowledge, or both, and illustrate their computation through an illustrative example. We also evaluate the application of the proposed approximation methods in the Machine Learning setting by showing that the approximation, through the proposed methods, of IFS k‐Nearest Neighbors is able to outperform, in terms of running time, the standard algorithm.

中文翻译：

---

直觉模糊集的基于熵的阴影集逼近

我们提出了一种用阴影集近似直觉模糊集 (IFS) 的方法，当不需要关于成员值的完整信息、难以处理或解释时，可以在决策或类似任务中使用该方法。我们的方法基于信息理论的观点，旨在通过最小化输入 IFS 和输出阴影集的熵之间的差异来保留原始 IFS 中由熵度量表示的不确定性。我们提出了三种不同的有效优化算法，它们保留了模糊性、缺乏知识或两者兼有，并通过一个说明性示例说明了它们的计算。我们还评估了所提出的近似方法在机器学习设置中的应用，方法是通过所提出的方法表明近似值，