Entropy-based shadowed set approximation of intuitionistic fuzzy sets

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 IFSk-Nearest Neighbors is able to outperform, in terms of running time, the standard algorithm.