Attribute reduction with fuzzy rough self-information measures

Hybrid similarity relation based mutual information for feature selection in intuitionistic fuzzy rough framework and its applications

Fuzzy rough entropy established in the notion of fuzzy rough set theory, which has been effectively and efficiently applied for feature selection to handle the uncertainty in real-valued datasets. Further, Fuzzy rough mutual information has been presented by integrating information entropy with fuzzy rough set to measure the importance of features. However, none of the methods till date can handle noise, uncertainty and vagueness simultaneously due to both judgement and identification, which lead to degrade the overall performances of the learning algorithms with the increment in the number of mixed valued conditional features. In the current study, these issues are tackled by presenting a novel intuitionistic fuzzy (IF) assisted mutual information concept along with IF granular structure. Initially, a hybrid IF similarity relation is introduced. Based on this relation, an IF granular structure is introduced. Then, IF rough conditional and joint entropies are established. Further, mutual information based on these concepts are discussed. Next, mathematical theorems are proved to demonstrate the validity of the given notions. Thereafter, significance of the features subset is computed by using this mutual information, and corresponding feature selection is suggested to delete the irrelevant and redundant features. The current approach effectively handles noise and subsequent uncertainty in both nominal and mixed data (including both nominal and category variables). Moreover, comprehensive experimental performances are evaluated on real-valued benchmark datasets to demonstrate the practical validation and effectiveness of the addressed technique. Finally, an application of the proposed method is exhibited to improve the prediction of phospholipidosis positive molecules. RF(h2o) produces the most effective results till date based on our proposed methodology with sensitivity, accuracy, specificity, MCC, and AUC of 86.7%, 90.1%, 93.0% , 0.808, and 0.922 respectively.

An Optimization Strategy for MADM Framework with Confidence Level Aggregation Operators under Probabilistic Neutrosophic Hesitant Fuzzy Rough Environment

In this research, we first offer unique notions of averaging and geometric aggregation operators with confidence level by employing a probabilistic neutrosophic hesitant fuzzy rough framework. Then, we look into other descriptions of the suggested operators, such as idempotency, boundedness, and monotonicity. Additionally, for the derived operators, we establish the score and accuracy functions. We also provide a novel approach to assessing the selection procedure for smart medical devices (SMDs). The selection criteria for SMDs are quite complex, which is the most noteworthy feature of this investigation. It is suggested that these processes be simulated using a method utilizing a hesitant fuzzy set, a rough set, and a probabilistic single-valued neutrosophics set. The proposed approach is employed in the decision-making process, while taking into consideration the decision-makers’ (DMs’) level of confidence in the data they have obtained in order to deal with ambiguity, incomplete data, and uncertainty in lower and upper approximations. The major goal was to outline the issue’s complexities in order to pique interest among experts in the health care sector and encourage them to evaluate SMDs using various evaluation standards. The analysis of the technique’s outcomes demonstrated that the rankings and the results themselves were adequate and trustworthy. The effectiveness of our suggested improvements is also demonstrated through a symmetrical analysis. The symmetry behavior shows that the current techniques address more complex and advanced data.

A deep network embedded with rough fuzzy discretization for OCT fundus image segmentation

The noise and redundant information are the main reasons for the performance bottleneck of medical image segmentation algorithms based on the deep learning. To this end, we propose a deep network embedded with rough fuzzy discretization (RFDDN) for OCT fundus image segmentation. Firstly, we establish the information decision table of OCT fundus image segmentation, and regard each category of segmentation region as a fuzzy set. Then, we use the fuzzy c-means clustering to get the membership degrees of pixels to each segmentation region. According to membership functions and the equivalence relation generated by the brightness attribute, we design the individual fitness function based on the rough fuzzy set, and use a genetic algorithm to search for the best breakpoints to discretize the features of OCT fundus images. Finally, we take the feature discretization based on the rough fuzzy set as the pre-module of the deep neural network, and introduce the deep supervised attention mechanism to obtain the important multi-scale information. We compare RFDDN with U-Net, ReLayNet, CE-Net, MultiResUNet, and ISCLNet on the two groups of 3D retinal OCT data. RFDDN is superior to the other five methods on all evaluation indicators. The results obtained by ISCLNet are the second only inferior to those obtained by RFDDN. DSC, sensitivity, and specificity of RFDDN are evenly 3.3%, 2.6%, and 7.1% higher than those of ISCLNet, respectively. HD95 and ASD of RFDDN are evenly 6.6% and 19.7% lower than those of ISCLNet, respectively. The experimental results show that our method can effectively eliminate the noise and redundant information in Oct fundus images, and greatly improve the accuracy of OCT fundus image segmentation while taking into account the interpretability and computational efficiency.

Feature selection based on self-information and entropy measures for incomplete neighborhood decision systems

For incomplete datasets with mixed numerical and symbolic features, feature selection based on neighborhood multi-granulation rough sets (NMRS) is developing rapidly. However, its evaluation function only considers the information contained in the lower approximation of the neighborhood decision, which easily leads to the loss of some information. To solve this problem, we construct a novel NMRS-based uncertain measure for feature selection, named neighborhood multi-granulation self-information-based pessimistic neighborhood multi-granulation tolerance joint entropy (PTSIJE), which can be used to incomplete neighborhood decision systems. First, from the algebra view, four kinds of neighborhood multi-granulation self-information measures of decision variables are proposed by using the upper and lower approximations of NMRS. We discuss the related properties, and find the fourth measure-lenient neighborhood multi-granulation self-information measure (NMSI) has better classification performance. Then, inspired by the algebra and information views simultaneously, a feature selection method based on PTSIJE is proposed. Finally, the Fisher score method is used to delete uncorrelated features to reduce the computational complexity for high-dimensional gene datasets, and a heuristic feature selection algorithm is raised to improve classification performance for mixed and incomplete datasets. Experimental results on 11 datasets show that our method selects fewer features and has higher classification accuracy than related methods.

Information entropy based attribute reduction for incomplete heterogeneous data

Attribute reduction in an information system (IS) is an important research topic in rough set theory (RST). This paper investigates attribute reduction for incomplete heterogeneous data based on information entropy. Information entropy in an incomplete IS with heterogeneous data (IISH) is first defined. Then, some derived notions of information entropy, such as joint information entropy, conditional information entropy, mutual information entropy, gain and gain ratio in an incomplete decision IS with heterogeneous data (IDISH), are presented. Next, information entropy is applied to perform attribute reduction in an IDISH. Two attribute reduction algorithms, based on gain and gain ratio, respectively, are proposed. Finally, in order to illustrate the feasibility and efficiency of the proposed algorithms, experimental analysis is carried out and comparisons are done. It is worth mentioning that the incomplete rate is used to deal with incomplete heterogeneous data.

Noise-Tolerant Discrimination Indexes for Fuzzy ɣ Covering and Feature Subset Selection

Fuzzy β covering (FBC) has attracted considerable attention in recent years. Nevertheless, as the basic information granularity of FBC, fuzzy β neighborhood does not satisfy reflexivity, which may lead to instability in classification learning and decision-making. Although a few studies have involved reflexive fuzzy β neighborhoods, they only focus on a single fuzzy covering and cannot effectively deal with the information representation and information fusion of multiple fuzzy coverings. Moreover, there is a lack of investigation on noise-tolerant uncertainty measures for FBC, as well as their application in feature selection. Motivated by these issues, we investigate a noise-tolerant variable precision discrimination index (VPDI) by means of a new reflexive fuzzy covering neighborhood. To this end, fuzzy ɣ neighborhood with reflexivity is introduced to characterize the information fusion of a fuzzy covering family. An uncertainty measure called fuzzy ɣ neighborhood discrimination index is then presented to reflect the discriminatory power of fuzzy covering families. Some variants of the uncertainty measure, such as variable precision joint discrimination index, variable precision conditional discrimination index, and variable precision mutual discrimination index, are then put forth by means of fuzzy decision. These VPDIs can be used as an evaluation metric for a family of fuzzy coverings. Finally, the knowledge reduction of fuzzy covering decision systems is addressed from the point of keeping the discriminatory power, and a heuristic feature selection algorithm is designed by means of the variable precision conditional discrimination index. The experiments on 16 public datasets exhibit that the proposed algorithm can effectively reduce redundant features and achieve competitive results compared with six state-of-the-art feature selection algorithms. Moreover, it demonstrates strong robustness to the interference of random noise.

A novel intuitionistic fuzzy rough set model and its application to enhance umami peptide prediction

Datasets mainly consist of ambiguous objects, redundant and uncertain attribute values which increase complexity, time and cost in Knowledge Discovery in Databases (KDD) process. Rough set-based attribute reduction techniques deals with ambiguity but fails to handle uncertainty available in a real-valued dataset. Combining rough set with intuitionistic fuzzy set provides a great opportunity to the researchers working on attribute reduction of real-valued datasets as it provides better results when compared to the traditional fuzzy rough set theory. In this paper, we present a new intuitionistic fuzzy rough set model for attribute reduction to avoid misclassification and perturbation by handling hesitancy, ambiguity and uncertainty present in a dataset. We define an intuitionistic fuzzy tolerance relation between two objects along with lower and upper approximations based on that relation. Next, the concept of Degree of dependency is utilized to present attribute reduction by using model due to its better performing nature over other methods. The algorithm of the proposed technique is applied on benchmark datasets to perform a comparative study with recent approaches. We obtain the best result for the reduced Breast Cancer dataset by our proposed approach, with an accuracy of 98.96% along with 0.90 standard deviation by using SMO classifier. Finally, our proposed method is used to present a methodology to improve the prediction of umami peptides. Here, we record the best results with sensitivity, specificity, accuracy, AUC, and MCC of 96.8%, 93.6%, 97.7%, 0.988, and 0.899, respectively. From the experiments, it can be concluded that our method outperforms the existing methods.

Generalized fuzzy variable precision rough sets based on bisimulations and the corresponding decision-making

Recently, the classical rough set has been extended in many ways. However, some of them are based on binary relations which only excavate “one step” information to distinguish objects. The “one step” in the binary relation means that the ordered pair of the starting and end points of the step belongs to the relation. Faced with some complex data sets, the “one step” information may be not feasible. Motivated by the notion of bisimulation in computer science, three types of bisimulation-based generalized fuzzy variable precision rough set (BGFVPRS) models are constructed. Different from many existed rough set models which are based on binary relations, the BGFVPRS models can distinguish objects by excavating the “multi-step” information of underlying relations. The related properties and relationships of BGFVPRS models are investigated. The uncertainty measure of BGFVPRS models and the reduction of fuzzy bisimulations are also discussed. Furthermore, learning from the PROMETHEE II method and combining it with our presented BGFVPRS models, a novel multiple-attribute decision-making method is provided. This method can effectively deal with complex problems including attribute data and relational data. The flexibility and effectiveness of our decision-making method are illustrated by comparative analysis and sensitivity analysis in the Zachary karate club network.

A Feature Selection Algorithm Integrating Maximum Classification Information and Minimum Interaction Feature Dependency Information

Feature selection is the key step in the analysis of high-dimensional small sample data. The core of feature selection is to analyse and quantify the correlation between features and class labels and the redundancy between features. However, most of the existing feature selection algorithms only consider the classification contribution of individual features and ignore the influence of interfeature redundancy and correlation. Therefore, this paper proposes a feature selection algorithm for nonlinear dynamic conditional relevance (NDCRFS) through the study and analysis of the existing feature selection algorithm ideas and method. Firstly, redundancy and relevance between features and between features and class labels are discriminated by mutual information, conditional mutual information, and interactive mutual information. Secondly, the selected features and candidate features are dynamically weighted utilizing information gain factors. Finally, to evaluate the performance of this feature selection algorithm, NDCRFS was validated against 6 other feature selection algorithms on three classifiers, using 12 different data sets, for variability and classification metrics between the different algorithms. The experimental results show that the NDCRFS method can improve the quality of the feature subsets and obtain better classification results.

An improved D-S evidence theory based neighborhood rough classification approach

Neighborhood classifier, a common classification method, is applied in pattern recognition and data mining. The neighborhood classifier mainly relies on the majority voting strategy to judge each category. This strategy only considers the number of samples in the neighborhood but ignores the distribution of samples, which leads to a decreased classification accuracy. To overcome the shortcomings and improve the classification performance, D-S evidence theory is applied to represent the evidence information support of other samples in the neighborhood, and the distance between samples in the neighborhood is taken into account. In this paper, a novel attribute reduction method of neighborhood rough set with a dynamic updating strategy is developed. Different from the traditional heuristic algorithm, the termination threshold of the proposed reduction algorithm is dynamically optimized. Therefore, when the attribute significance is not monotonic, this method can retrieve a better value, in contrast to the traditional method. Moreover, a new classification approach based on D-S evidence theory is proposed. Compared with the classical neighborhood classifier, this method considers the distribution of samples in the neighborhood, and evidence theory is applied to describe the closeness between samples. Finally, datasets from the UCI database are used to indicate that the improved reduction can achieve a lower neighborhood decision error rate than classical heuristic reduction. In addition, the improved classifier acquires higher classification performance in contrast to the traditional neighborhood classifier. This research provides a new direction for improving the accuracy of neighborhood classification.