Fuzzy Rough Set Theory Research Articles

Measures of uncertainty for a fuzzy probabilistic approximation space

An approximation space (A-space) is the base of rough set theory and a fuzzy approximation space (FA-space) can be seen as an A-space under the fuzzy environment. A fuzzy probability approximation space (FPA-space) is obtained by putting probability distribution into an FA-space. In this way, it combines three types of uncertainty (i.e., fuzziness, probability and roughness). This article is devoted to measuring the uncertainty for an FPA-space. A fuzzy relation matrix is first proposed by introducing the probability into a given fuzzy relation matrix, and on this basis, it is expanded to an FA-space. Then, granularity measurement for an FPA-space is investigated. Next, information entropy measurement and rough entropy measurement for an FPA-space are proposed. Moreover, information amount in an FPA-space is considered. Finally, a numerical example is given to verify the feasibility of the proposed measures, and the effectiveness analysis is carried out from the point of view of statistics. Since three types of important theories (i.e., fuzzy set theory, probability theory and rough set theory) are clustered in an FPA-space, the obtained results may be useful for dealing with practice problems with a sort of uncertainty.

A fuzzy-rough uncertainty measure to discover bias encoded explicitly or implicitly in features of structured pattern classification datasets

The need to measure bias encoded in tabular data that are used to solve pattern recognition problems is widely recognized by academia, legislators and enterprises alike. In previous work, we proposed a bias quantification measure, called fuzzy-rough uncer-tainty, which relies on the fuzzy-rough set theory. The intuition dictates that protected features should not change the fuzzy-rough boundary regions of a decision class significantly. The extent to which this happens is a proxy for bias expressed as uncertainty in adecision-making context. Our measure's main advantage is that it does not depend on any machine learning prediction model but adistance function. In this paper, we extend our study by exploring the existence of bias encoded implicitly in non-protected featuresas defined by the correlation between protected and unprotected attributes. This analysis leads to four scenarios that domain experts should evaluate before deciding how to tackle bias. In addition, we conduct a sensitivity analysis to determine the fuzzy operatorsand distance function that best capture change in the boundary regions.

An Ensemble-Based Fuzzy Rough Active Learning Approach for Broken Rotor Bar Detection in Nonstationary Environment

Most existing fault detection methods rely on batch learning, which assumes that all data is available and can be accessed over and over again. Such an approach is impossible in the face of nonstationary environments. This paper proposes an online combination of an Ensemble framework, Fuzzy Rough Active Learning, and drift detection, namely EFRAL, in which the structure of the ensemble automatically grows according to the data distribution. Since obtaining a real industrial data label is costly and time-consuming in practice, this paper incorporates an active learning scenario based on fuzzy rough sets to reduce operator labeling effort. This method gives weight to training samples based on the fuzzy rough sets theory and the samples are selected based on their weight. The proposed algorithm is applied to detect a broken rotor bar fault of induction motors to show its feasibility in industrial environments. The attained results show the efficiency of the proposed method. Furthermore, the efficiency of EFRAL is evaluated through data stream problems.

Adaptive Fuzzy Learning Superpixel Representation for PolSAR Image Classification

The increasing applications of polarimetric synthetic aperture radar (PolSAR) image classification demand for effective superpixels’ algorithms. Fuzzy superpixels’ algorithms reduce the misclassification rate by dividing pixels into superpixels, which are groups of pixels of homogenous appearance and undetermined pixels. However, two key issues remain to be addressed in designing a fuzzy superpixel algorithm for PolSAR image classification. First, the polarimetric scattering information, which is unique in PolSAR images, is not effectively used. Such information can be utilized to generate superpixels more suitable for PolSAR images. Second, the ratio of undetermined pixels is fixed for each image in the existing techniques, ignoring the fact that the difficulty of classifying different objects varies in an image. To address these two issues, we propose a polarimetric scattering information-based adaptive fuzzy superpixel (AFS) algorithm for PolSAR images classification. In AFS, the correlation between pixels’ polarimetric scattering information, for the first time, is considered through fuzzy rough set theory to generate superpixels. This correlation is further used to dynamically and adaptively update the ratio of undetermined pixels. AFS is evaluated extensively against different evaluation metrics and compared with the state-of-the-art superpixels’ algorithms on three PolSAR images. The experimental results demonstrate the superiority of AFS on PolSAR image classification problems.

Uncertainty instructed multi-granularity decision for large-scale hierarchical classification

Hierarchical classification identifies a sample from the root node to a leaf node along the hierarchical structures of labels. It is often difficult to perform leaf-node prediction owing to ambiguous or incomplete information In such scenarios, a multi-granularity decision needs to be designed to stop the sample at a coarse-grained node rather than going rashly to a wrong leaf node. Conventionally, the probabilities of assigning the sample to its child nodes are regarded as evidence to decide whether to let the sample stop or go. However, the fact that the output of an unreliable classifier cannot be used to appropriately form the basis of decision making, especially with the existence of data uncertainties, is overlooked by existing methods. Therefore, we model the multi-granularity decision problem from an uncertainty perspective and consider that the uncertainties of multi-granularity decision emanate from the prediction of the classifier and the intrinsic information of the data. Inspired by the theory of fuzzy rough sets, a new measure is proposed to describe the intrinsic uncertainty in data. Integrating with the prediction uncertainty of the classifier, the hierarchical structure is used to design an effective optimization method that ensures proper multi-granularity decisions. Experiments show that the proposed algorithm achieves state-of-the-art performance.

A relative uncertainty measure for fuzzy rough feature selection

Uncertainty measure is an important tool for data analysis. In practical applications, the collected data are subject to different probability distributions. This requires that the uncertainty measure has generalization performance. Fuzzy rough set (FRS) theory is a popular mathematical tool for uncertainty measure, but the theory does not work well for some data distributions. For example, when the class density difference of the data set is large, FRS theory cannot effectively evaluate the classification uncertainty of samples. In this study, we combine the relative measure with the lower approximation of FRSs to propose a relative uncertainty measure which can address the above-mentioned problem. Furthermore, a fuzzy rough feature selection algorithm is designed, and it is mainly used to test the effectiveness and efficiency of the proposed measure. Experimental results demonstrate that the proposed feature selection algorithm has good performance. It indirectly proves that the relative uncertainty measure is effective and efficient in classification tasks.

An Efficient Classification Model using Fuzzy Rough Set Theory and Random Weight Neural Network

In the area of fuzzy rough set theory (FRST), researchers have gained much interest in handling the high-dimensional data. Rough set theory (RST) is one of the important tools used to pre-process the data and helps to obtain a better predictive model, but in RST, the process of discretization may loss useful information. Therefore, fuzzy rough set theory contributes well with the real-valued data. In this paper, an efficient technique is presented based on Fuzzy rough set theory (FRST) to pre-process the large-scale data sets to increase the efficacy of the predictive model. Therefore, a fuzzy rough set-based feature selection (FRSFS) technique is associated with a Random weight neural network (RWNN) classifier to obtain the better generalization ability. Results on different dataset show that the proposed technique performs well and provides better speed and accuracy when compared by associating FRSFS with other machine learning classifiers (i.e., KNN, Naive Bayes, SVM, decision tree and backpropagation neural network).

Axiomatic characterizations of [formula omitted]-valued rough sets using a single axiom

Fuzzy rough approximation operators are the underlying concepts in fuzzy rough set theory. There are at least two approaches to develop these primary concepts, i.e., the constructive approach and the axiomatic approach. Single axiomatic characterizations of fuzzy rough approximation operators have got tons of attention. In this paper, considering L being a GL-quantale, we will develop the theory of L-valued rough sets with an L-set as the basic universe of defining L-valued rough approximation operators. Adopting the idea of single axiomatic characterizations of fuzzy rough sets, we will present the axiomatic characterizations of L-valued upper and lower rough approximation operators on an L-set with respect to reflexive, symmetric, transitive L-valued relations on an L-set as well as their compositions. Choosing an L-set as the universe will break the rules that adopting Zadeh’s fuzzy sets as the universe. By these results, we will further provide a new framework of axiomatic research of fuzzy rough set theory.

Fuzzy complementary entropy using hybrid-kernel function and its unsupervised attribute reduction

Fuzzy rough set theory has been proved to be an effective tool to deal with uncertainty data. Some different forms of fuzzy uncertainty measures have been introduced in fuzzy rough set theory, such as fuzzy information entropy, fuzzy conditional entropy, and fuzzy mutual information. However, as far as we know, most of the above fuzzy conditional entropy and fuzzy mutual information are non-monotonic, which may lead to a non-convergent learning algorithm. For this reason, this paper proposes a novel fuzzy complementary entropy based on the hybrid-kernel function. Then, based on the proposed fuzzy complementary entropy, some corresponding uncertainty measures are also proposed. Furthermore, fuzzy complementary conditional entropy and fuzzy complementary mutual information are proved to change monotonously with attributes. Finally, based on the proposed uncertainty measures, three kinds of evaluation criteria for unsupervised hybrid attribute reduction are defined and a generalized attribute reduction algorithm is designed. The experimental results show that the proposed method is an effective scheme for reducing hybrid attributes.

Predicting users’ preferences by Fuzzy Rough Set Quarter-Sphere Support Vector Machine

Recommender systems aim to support users in decision-making through the knowledge extracted from historical ratings. However, many of these ratings may be noisy and/or missing, causing degradation in the quality of the recommendations. Considering these issues, this paper presents a new one-class classifier to predict ratings in recommendation systems. The proposed method estimates the shared informative neighbors of each user by a probability fuzzy rough set method. Since the fuzzy rough set theory is sensitive to noisy samples, the quarter-sphere SVM classifier is designed to reduce the impact of noise on the results. The proposed classifier can satisfactorily determine a boundary around the target class while it reduces the acceptance probability of the outliers and non-target class(es). The theoretical interpretations are provided to prove the statistical stability of the proposed method. Also, noise analysis has been carried out. Through extensive experiments on several real-world data sets, it is confirmed that the proposed method outperforms the other six methods in terms of accuracy, recall, precision, and computational time.

( 2005-5897) Different classes ratio and Laplace summation operator based intuitionistic fuzzy rough attribute selection

In real-world data deluge, due to insignificant information and high dimension, irrelevant and redundant attributes reduce the ability of experts both in predictive accuracy and speed, respectively. Attribute selection is the notion of selecting those attributes that are essential as well as enough to specify the target knowledge preferably. Fuzzy rough set-based approaches play a crucial role in selecting relevant and less redundant attributes from a high-dimensional dataset. Intuitionistic fuzzy set-based approaches can handle uncertainty as it gives an additional degree of freedom when compared to fuzzy approaches. So, it has a more flexible and practical ability to deal with vagueness and noise available in the information system. In this paper, we introduce two new robust approaches for attribute selection based on intuitionistic fuzzy rough set theory using the concepts of Different Classes ratio and Laplace Summation operator. Firstly, Different Classes ratio and Laplace Summation operator based lower andupper approximations are established based on intuitionistic fuzzy rough set concept. Moreover, we present algorithms and illustrative examples for a better understanding of our approaches. Finally, experimental analysis is performed on some real-valued datasets for attribute selection and classification accuracies.

Material–Structure–Process–Performance Integration Multi-Objective Optimization Design for Solid Rivet Joint

A material–structure–process–performance integration multi-objective optimization design of a magnesium/aluminum alloy punch-forming solid rivet joint based on Taguchi, grey relational analysis (GRA), and fuzzy rough set theory (FRST) weighting method was proposed. First, the material constitutive models of the rivet and riveted sheets were established through experiments. Second, simulation models of the rivet forming process and the pull-out and shear tests of the riveted joint were established, and corresponding experiments verified accuracy. Finally, the FRST weighting method was proposed. The integration multi-objective optimization of a rivet joint was conducted based on Taguchi, GRA, and FRST methods with optimization objectives (the rivet forming head’s dimensions and the riveted joint’s maximum pull-out and shear forces) and design variables (the material, structure, and riveting process parameters of the rivet joint). The optimal combination of design variable levels was obtained. Optimization results show that the rivet forming head’s dimensions were quite close to the recommended values after optimization, and the pull-out and shear mechanical strengths of the riveted joint were increased by 10.7% and 12.8%, respectively. Furthermore, a comparison was presented among FRST, principal component analysis, and entropy weighting methods. The FRST weighting method was concluded to be highly effective.

Fuzzy Rough Set Theory (FRST) Classifier for Pest Prediction in India

Total cotton production is affected by an important factor called cotton pests occurrence. During the growth of cotton, environmental factors having great dependence especially during climate change. In multi-disciplinary agri-technologies domain, for data intensive science, for creating new opportunities, machine learning with big data technologies is used as a high-performance computing technique and good results are produced using this. However, running time and accuracy are highly important task. Affected crop pests are only predicted using available machine learning techniques. But there wont be any accurate level of pest affection by cotton. In this paper, proposed a Fuzzy Rough Set Theory (FRST) for handling this pest prediction level. There are four major steps in this proposed work, namely, results evaluation, prediction, pre-processing and dataset collection. From 2010-2020, from All India Coordinated Research Project (AICRP) collected the dataset in the first stage. Irrelevant features are removed by performing pre-processing in the second stage and for prediction, needed features only considered. However, for prediction, weather parameters like Rainfall (RF), Relative Humidity-Evening(RH-E), Relative Humidity-Morning(RH-M), Minimum Temperature(Min-Temp) and Maximum Temperature(Max-Temp) are used. For pest prediction, only these weather parameters are used and from original dataset removed the remaining parameters. This produces a pre-processed dataset. For pest prediction, proposed a Fuzzy Rough Set Theory (FRST) classifier in third step. Cotton pest pre-processed dataset is used for training FRST. Activation corresponds to high approximation and lower approximation functions. Weather factors belonging to higher cotton pests are predicted in this result. For future pest, FRST network can be used as a better predictor according to pest records. Moreover, better performance is shown by proposed FRST network, when compared with traditional machine learning techniques like Random Forest (RF) and Multi-Layer Perceptron (MLP). At last, these pest prediction techniques effectiveness is measured using metrics like F-measure, Area Under the Curve (AUC), and Accuracy (ACC).

MapReduce based parallel fuzzy-rough attribute reduction using discernibility matrix

Fuzzy-rough set theory is an efficient method for attribute reduction. It can effectively handle the imprecision and uncertainty of the data in the attribute reduction. Despite its efficacy, current approaches to fuzzy-rough attribute reduction are not efficient for the processing of large data sets due to the requirement of higher space complexities. A limited number of accelerators and parallel/distributed approaches have been proposed for fuzzy-rough attribute reduction in large data sets. However, all of these approaches are dependency measure based methods in which fuzzy similarity matrices are used for performing attribute reduction. Alternative discernibility matrix based attribute reduction methods are found to have less space requirements and more amicable to parallelization in building parallel/distributed algorithms. This paper therefore introduces a fuzzy discernibility matrix-based attribute reduction accelerator (DARA) to accelerate the attribute reduction. DARA is used to build a sequential approach and the corresponding parallel/distributed approach for attribute reduction in large data sets. The proposed approaches are compared to the existing state-of-the-art approaches with a systematic experimental analysis to assess computational efficiency. The experimental study, along with theoretical validation, shows that the proposed approaches are effective and perform better than the current approaches.

Research on Optimal Operation of Electricity Heat Hydrogen System Based on Evaluation of New Energy Consumption Potential

Under the background of the “double high” power system, the electricity heat hydrogen system (EHHS) plays a significant role in the process of energy decarbonization. In order to meet the different optimization objectives of the system under different new energy consumption states, a new energy consumption potential assessment and optimized operation method based on intuitionistic fuzzy rough set theory is proposed. By using the intuitionistic fuzzy rough set theory, the continuous attribute data is divided into different levels and the results of its membership and non-membership are gotten at different levels. The membership results of real-time consumption data are matched with the rule sets, and then the system consumption state judgment result is obtained. In this article, the system consumption situation is divided into five states, and compared with the traditional division method, so the system state can be described more comprehensively. At the same time, the fuzzy set is used to deal with the ambiguity of the boundary between each state. The intuition theory is used to solve the problem of the uncertainty of the consumption state, and then the accurate judgment can be realized. In response to different consumption states, an optimal scheduling model is established in which a hydrogen heat energy system (HHES) is involved to meet different requirements, and a hybrid particle swarm optimization algorithm is used to solve the model. Adopting the IEEE-30 bus system as the network structure of EHHS in the simulation, the analysis shows that the dynamic state division method based on intuitionistic fuzzy rough set theory can better be used to judge the system state according to real-time variable factors. The system optimization based on the consumption state division has the advantages of improving the operating economy and increasing the consumption of new energy.

Weighted support vector machine using fuzzy rough set theory

The existence of both uncertainty and imprecision has detrimental impact on efficiency of decision-making applications and some machine learning methods, in particular support vector machine in which noisy samples diminish the performance of SVM training. Therefore, it is important to introduce a special method in order to improve this problem. Fuzzy aspects can handle mentioned problem which has been considered in some classification methods. This paper presents a novel weighted support vector machine to improve the noisy sensitivity problem of standard support vector machine for multiclass data classification. The basic idea is considered to add a weighted coefficient to the penalty term Lagrangian formula for optimization problem, which is called entropy degree, using lower and upper approximation for membership function in fuzzy rough set theory. As a result, noisy samples have low degree and important samples have high degree. To evaluate the power of the proposed method WSVM-FRS (Weighted SVM-Fuzzy Rough Set), several experiments have been conducted based on tenfold cross-validation over real-world data sets from UCI repository and MNIST data set. Experimental results show that the proposed method is superior than the other state-of-the-art competing methods regarding accuracy, precision and recall metrics.

Covering-based variable precision L-fuzzy rough sets based on residuated lattices and corresponding applications

There are many extensions of Pawlak’s rough sets. Particularly, fuzzy rough set theory based on residuated lattices is considered as one of the generalizations that extends the truth values to lattices. In this paper, we attempt to combine the idea of “variable precision” with covering-based fuzzy rough sets based on residuated lattices and present the concept of covering-based variable precision L-fuzzy rough sets. After the presentation of this concept, some basic properties of the proposed rough set model are discussed. Then, with the aid of the PROMETHEE and TOPSIS methods, we put forth a novel multi-attribute decision-making (MADM) method based on covering-based variable precision L-fuzzy rough sets (for $$L=[0,1]$$ ). Finally, an illustrative example is give to demonstrate the proposed decision-making method. By a sensitivity analysis along with a comparative analysis, we reveal the applicability and validity of the proposed decision-making method.

Construction of an AI-Driven Risk Management Framework for Financial Service Firms Using the MRDM Approach

The complex problem of risk factors has greatly increased globally due to the quick ever-changing digital era. The development of suitable techniques for facilitating the performance of risk management in the financial service domain is thus an urgent task, especially in today’s highly turbulent business environment. The development of such techniques involves many factors like the classical multiple criteria decision-making (MCDM) problem, but too many factors surrounding the users will confuse them and lead to improper judgments. To deal with this critical task, this study proposes a fusion multiple rule-based decision-making (MRDM) approach that integrates a rule-based technique [i.e., the fuzzy rough set theory (FRST) with particle swarm optimization (PSO)] into MCDM (i.e., DEMATEL, DANP, and modified-VIKOR) techniques that can help decision makers choose the optimal model necessary for achieving aspiration-level effects in a risk control strategy. The results indicate that the improvement priority, which runs in the order as (a) AI algorithm model, (c) AI regulatory and compliance, (d) AI conduct, and (b) AI technology based on the magnitude of the impact, can effectively improve the performance of AI-driven risk management for financial service firms.

Attribute reduction methods in fuzzy rough set theory: An overview, comparative experiments, and new directions

Fuzzy rough set theory is a powerful tool to deal with uncertainty information, which has been successfully applied to the fields of attribute reduction, rule extraction, classification tree induction, etc. In order to comprehensively investigate attribute reduction methods in fuzzy rough set theory, this paper first briefly reviews the related concepts of fuzzy rough set theory. Then, all methods are summarized through six different aspects including data sources, preprocessing methods, fuzzy similarity metrics, fuzzy operations, reduction rules, and evaluation methods. Among them, reduction rules are reviewed in three categories, i.e., fuzzy dependency-based, fuzzy uncertainty measure-based, and fuzzy discernibility matrix-based. These three types of reduction rules are compared and analyzed through experiments. The experimental results clarify that these three reduction rules can retain fewer attributes and improve or maintain the classification accuracy of a classifier. Moreover, the statistical hypothesis test is conducted to evaluate the statistical difference of these methods. The results show that these algorithms are statistically significantly different. Finally, some new research directions are discussed.

Fuzzy distance-based filter-wrapper incremental algorithms for attribute reduction when adding or deleting attribute set

Attribute reduction is a critical problem in the data preprocessing step with the aim of minimizing redundant attributes to improve the efficiency of data mining models. The fuzzy rough set theory is considered an effective tool to solve the attribute reduction problem directly on the original decision system, without data preprocessing. With the current digital transformation trend, decision systems are larger in size and updated. To solve the attribute reduction problem directly on change decision systems, a number of recent studies have proposed incremental algorithms to find reducts according to fuzzy rough set approach to reduce execution time. However, the proposed algorithms follow the traditional filter approach. Therefore, the obtained reduct is not optimal in both criteria: the number of attribute of the reducts and the accuracy of classification model. In this paper, we propose incremental algorithms that find reducts following filter-wrapper approach using fuzzy distance measure in the case of adding and deleting attribute set. The experimental results on the sample datasets show that the proposed algorithms significantly reduce the number of attributes in reduct and improve the classification accuracy compared to other algorithms using filter approach