A Novel Method for Constructing Shadowed Set Based on Intuitionistic Fuzzy λ-Cut Set and Fuzzy Entropy

As a three-way approximation model for handling fuzzy information, shadowed set plays a significant role, it is targeted at effective approximate partitioning in objects with fuzzy information in intuitionistic fuzzy set. The shadowed set can not only improve the accuracy of decision task, but also effectively decrease the expense of decision task. However, the existing construction of shadowed set relies on intuitionistic fuzzy set, either emphasizing semantic interpretation rationality without considering partitioning validity, or focusing on high uncertainty objects without holistic fuzziness analysis. In order to address above problems, a novel shadowed set model (IF-CESS) is proposed in this paper. First, IF-CESS starts from the definition of shadowed set, and utilizes the characteristics of [Formula: see text]-cut sets that can divide intuitionistic fuzzy sets based on the inherent structure of fuzzy information. It converts fuzzy information into certain information and partial fuzzy information, and obtains different [Formula: see text]-cut sets for different [Formula: see text] thresholds. Second, the entropy of the intuitionistic fuzzy set and [Formula: see text]-cut sets is calculated. Third, by analyzing the fuzzy entropy loss between the intuitionistic fuzzy set and [Formula: see text]-cut sets, and selecting the threshold [Formula: see text] corresponding to the minimal entropy loss, which obtains to the shadowed set model. Finally, the construction process of IF-CESS is demonstrated through an example, and validity and rationality of IF-CESS are demonstrated through the data experiments of intuitionistic fuzzy KNN algorithm.