The study is concerned with the representation and aggregation of complex uncertainty information. First, the concept of hesitant Fermatean 2‐tuple linguistic sets (HF2TLSs) is introduced for characterizing an individual’s imprecision preferences and assessing information by combining 2‐tuple linguistic terms and Fermatean fuzzy sets. The advantage of hesitant Fermatean 2‐tuple linguistic information is that it can handle higher levels of uncertainty and express the decision‐makers’ hesitancy. Second, we extend Bonferroni mean (BM) operators under the background of HF2TLSs for the sake of their application in information fusion and decision making. The Archimedean t‐norm and s‐norm‐ (ATS‐) based hesitant Fermatean 2‐tuple linguistic weighted Bonferroni mean (A‐HF2TLWBM) operator and the ATS‐based hesitant Fermatean 2‐tuple linguistic weighted geometric Bonferroni mean (A‐HF2TLWGBM) operator are developed by considering the interrelationship between any two variables. The main benefit of the proposed operators is that these operators deliver more complete and flexible results compared to existing methods. Moreover, some fundamental properties and special cases are examined by adjusting parameter values. Finally, an approach is designed as a support for handling decision making problems, and an example regarding investment selection is provided to demonstrate the practicality of the designed method with a detailed discussion of parameter influence and comparisons with the existing methods.

Imbalance ensemble classification is one of the most essential and practical strategies for improving decision performance in data analysis. There is a growing body of literature about ensemble techniques for imbalance learning in recent years, the various extensions of imbalanced classification methods were established from different points of view. The present study is initiated in an attempt to review the state-of-the-art ensemble classification algorithms for dealing with imbalanced datasets, offering a comprehensive analysis for incorporating the dynamic selection of base classifiers in classification. By conducting 14 existing ensemble algorithms incorporating a dynamic selection on 56 datasets, the experimental results reveal that the classical algorithm with a dynamic selection strategy deliver a practical way to improve the classification performance for both a binary class and multi-class imbalanced datasets. In addition, by combining patch learning with a dynamic selection ensemble classification, a patch-ensemble classification method is designed, which utilizes the misclassified samples to train patch classifiers for increasing the diversity of base classifiers. The experiments’ results indicate that the designed method has a certain potential for the performance of multi-class imbalanced classification.

Introduction: Ubiquitylation, a key post-translational modification (PTM), has significant influences on the structures, activities, and functions of proteins and is linked to various diseases. Traditional experimental identification and characterization methods for identifying ubiquitylation sites (Ubsites) are time-consuming, expensive, and labor-intensive if prior knowledge concerning ubiquitylation is absent. Nevertheless, most methods reported for predictions of Ubsites are based on traditional machine learning. Owing to the increased availability of genomic and proteomic samples, deep learning-based recognition methods for Ubsites are becoming increasingly popular. Methods: In this study, we propose a new feature extraction method, pKcode, based on only seven physicochemical features of amino acids (AAs). The pKcode captures both the biochemical context and precise sequence locations of AAs around the Ubsites, improving the predictive capability for ubiquitination. We created the pKPAP encoding scheme by integrating the pKcode with PSDAAP, AAC, and PWAA, resulting in an all-encompassing feature representation. Concurrently, we developed the PKE-Ubsite model. Results: PKE-Ubsite model, a new ensemble prediction framework, amalgamates the power of classifiers in five pipelines: three bidirectional long short-term memory (BiLSTM) networks, one convolutional neural network (CNN), and one random forest (RF) classifier. Each classifier uses an optimized combination of encoding features, and an integrated classification is achieved through a voting mechanism. Conclusion: Finally, compared with existing models on an independent test set, our model has an accuracy of 0.8368, an F1-score of 0.8430, a precision of 0.8124, a recall of 0.8760, and an AUC of 0.9103, which are superior to all methods reported to date. Overall, PKE-Ubsite may facilitate a thorough understanding of ubiquitylation.