A method for constructing an optimistic shadowed set based on intuitionistic fuzzy knowledge measure and λ-cut set

As a three-way approximation model for handling fuzzy information, shadowed sets are effectively utilized to approximate and partition uncertain objects within the fuzzy information. Thus, the uncertainty loss associated with sample-decision partitioning in the fuzzy decision-making process is reduced by the shadowed sets. The existing shadowed sets based on intuitionistic fuzzy sets are constructed utilizing the loss of intuitionistic fuzzy entropy. However, the objects within the intuitionistic fuzzy set are not accurately distinguished by the intuitionistic fuzzy entropy, and the shadow region of the shadowed set model is characterized by higher uncertainty, with the information provided by the objects in that region not being fully utilized. To solve these issues, an optimistic shadowed set model (IFS-KCSS) is proposed in this paper, based on intuitionistic fuzzy knowledge measure (KM) and λ -cut sets. First, the KM of the intuitionistic fuzzy set is calculated to measure its information content. Second, the intuitionistic fuzzy set is divided into multiple λ -cut sets according to different thresholds, and the loss of KM between each λ -cut set and the original intuitionistic fuzzy set is calculated. Third, the λ -cut set with the minimum loss of KM is selected as the shadowed set which contains elevated region, shadow region, and reduced region. Subsequently, the remaining objects within the shadow region are further subdivided using the corresponding threshold, resulting in the construction of IFS-KCSS that contains two precise regions. Finally, the proposed optimistic shadowed set model (IFS-KCSS) is applied to the classifcation algorithm of the Multilayer Perceptron (MLP), and comparisons across multiple indicators on six datasets verify its rationality.