Fuzzy Rough Set Theory Research Articles

An optimization strategy with SV-neutrosophic quaternion information and probabilistic hesitant fuzzy rough Einstein aggregation operator

<abstract><p>The single valued neutrosophic probabilistic hesitant fuzzy rough Einstein aggregation operator (SV-NPHFRE-AO) is an extension of the neutrosophic probabilistic hesitant fuzzy rough set theory. It is a powerful decision-making tool that combines the concepts of neutrosophic logic, probability theory, hesitant fuzzy sets, rough sets, and Einstein aggregation operators. SV-NPHFRE-AO can be applied in many fields, including livestock decision making. Making judgments about a wide range of issues, including feed formulation, breeding program design, disease diagnostics, and market analysis, is part of the process of managing livestock. By combining data from many sources, SV-NPHFRE-AO can assist decision-makers in livestock management in integrating and evaluating diverse criteria, which can result in more informed choices. It also provides a more accurate and comprehensive representation of decision-making problems by considering the multiple criteria involved and the relationships between them. The single valued neutrosophic set (SV-NS) aggregation operators (AOs) based on Einstein properties using hesitant fuzzy sets (HFSs) and probabilistic hesitant fuzzy sets (PHFSs) with rough sets (RSs) are proposed in this study and can handle a large volume of data, making them suitable for complex and large-scale livestock decision-making problems. We first defined SV-neutrosophic probabilistic hesitant fuzzy rough weighted averaging (SV-NPHFRWA), SV-neutrosophic probabilistic hesitant fuzzy rough weighted geometric (SV-NPHFRWG), SV-neutrosophic probabilistic hesitant fuzzy rough ordered weighted averaging (SV-NPHFROWA) and SV-neutrosophic probabilistic hesitant fuzzy rough hybrid weighted averaging (SV-NPHFRHWA) AOs. Then, based on Einstein properties, we extended these operators and developed the single-valued neutrosophic probabilistic hesitant fuzzy rough Einstein weighted averaging (SV-NPHFREWA) operator. Additionally, an illustrative scenario to show the applicability of the suggested decision-making approach is provided, along with a sensitivity analysis and comparison analysis, which demonstrate that its outcomes are realistic and reliable. We also provide another relation between criteria and alternatives of decision-making using neutrosophic information with quaternion context. By using such type of operators, livestock managers can make more informed decisions, leading to better animal health, higher productivity, and increased profitability.</p></abstract>

Prolog-based agnostic explanation module for structured pattern classification

This paper presents a Prolog-based reasoning module to generate counterfactual explanations given the predictions computed by a black-box classifier. Our approach comprises four well-defined stages that can be applied to any structured pattern classification problem. Firstly, we pre-process the given dataset by imputing missing values and normalizing the numerical features. Secondly, we transform numerical features into symbolic ones using fuzzy clustering such that extracted fuzzy clusters are mapped to an ordered set of predefined symbols. Thirdly, we encode instances as a Prolog rule using the nominal values, the predefined symbols, the decision classes, and the confidence values. Fourthly, we compute the overall confidence of each Prolog rule using fuzzy-rough set theory to handle the uncertainty caused by transforming numerical quantities into symbols. This step comes with an additional theoretical contribution to a new similarity function to compare the previously defined Prolog rules involving confidence values. Finally, we implement a chatbot as a proxy between humans and the Prolog-based reasoning module to resolve natural language queries and generate counterfactual explanations. During the numerical simulations using synthetic datasets, we study the performance of our system when using different fuzzy operators and similarity functions.

Connectivity-Based Localization Scheme for Social Internet of Things

Different from the social network which only focuses on the interaction between people, the integration of social networks and the internet of things (IoT) leads to multi-directional interactions of human to human, human to thing, and thing to thing. The social IoT is composed of a large number of heterogeneous devices, which can improve the scalability of resource and service. Meanwhile, the heterogeneous devices have uneven computing power and different location information measurement types (e.g., the distance, angle, and hop count). Therefore, a localization approach with easy-to-obtain measurement data and low requirements on the computing power is needed. In this article, we propose a localization approach for the social IoT by combining the fuzzy rough set theory and the ridge regression extreme learning machine (RRELM). First of all, a location fingerprint database is constructed. Different from the traditional location fingerprint database, the location fingerprint database here stores the minimum hop counts between the reference node (RN) and the anchor node (AN) instead of the received signal strength (RSS). Second, the fuzzy rough set theory is used to compute the significant degree of each AN, and the ANs that contribute little to the positioning result are removed. This approach not only relieves the storage pressure of the location fingerprint database but also reduces the computational complexity of user position estimation. Third, the RRELM is trained by using the samples in the location fingerprint database. Finally, by inputting the newly collected minimum hop counts from the user to each AN into the trained RRELM, the user’s position is estimated. From the extensive experimental results, the proposed approach has high positioning accuracy and low computational complexity, which is suitable for the social IoT.

Noise-resistant multilabel fuzzy neighborhood rough sets for feature subset selection

Feature selection attempts to capture the more discriminative features and plays a significant role in multilabel learning. As an efficient mathematical tool to handle incomplete and uncertain information, fuzzy rough set theory has been widely used in feature selection. However, there are two pivotal issues to be addressed when adopting fuzzy rough sets for multilabel data analysis. One is how to effectively characterize the discriminative ability of the features to multilabel samples. Another one is how to alleviate the effect of data noise on feature selection. For these reasons, this study mainly studies the noise-tolerant fuzzy neighborhood rough set model for multilabel learning and its feature selection strategy. Firstly, a parameterized hybrid fuzzy similarity relation is introduced to granulate multilabel data, and the parameterized fuzzy decision is extended to multilabel learning. Then, a noise-resistant multilabel fuzzy neighborhood rough set model using inclusion relation is constructed for describing the discriminative ability of the features to multilabel samples. Furthermore, a noise-resistant heuristic feature selection algorithm titled NRFSFN is designed. Besides, motivated by local sampling and ensemble strategy, an efficient extended version of NRFSFN is designed from the perspective of data distribution, named ENFSFN. Finally, a series of comparison experiments on sixteen multilabel datasets demonstrate the effectiveness of the proposed two algorithms.

Rough-Fuzzy CPD: a gradual change point detection algorithm

Changepoint detection is the problem of finding abrupt or gradual changes in time series data when the distribution of the time series changes significantly. There are many sophisticated statistical algorithms for solving changepoint detection problem, although there is not much work devoted towards gradual changepoints as compared to abrupt ones. Here we present a new approach to solve the changepoint detection problem using the fuzzy rough set theory which is able to detect such gradual changepoints. An expression for the rough-fuzzy estimate of changepoints is derived along with its mathematical properties concerning fast computation. In a statistical hypothesis testing framework, the asymptotic distribution of the proposed statistic on both single and multiple changepoints is derived under the null hypothesis enabling multiple changepoint detection. Extensive simulation studies have been performed to investigate how simple crude statistical measures of disparity can be subjected to improve their efficiency in the estimation of gradual changepoints. Also, the said rough-fuzzy estimate is robust to signal-to-noise ratio, a high degree of fuzziness in true changepoints, and also to hyperparameter values. Simulation studies reveal that the proposed method beats other methods of gradual changepoint detection (including MJPD, HSMUCE, fuzzy methods like FCP, FCMLCP etc) and also popular crisp methods like Binary Segmentation, PELT, and BOCD in detecting gradual changepoints. The applicability of the estimate is demonstrated using multiple real-life datasets including Covid-19. We have developed the python package roufcp for broader dissemination of the methods.

An exploration of the key determinants for the application of AI-enabled higher education based on a hybrid Soft-computing technique and a DEMATEL approach

The application of AI in higher education has greatly increased globally in the dynamic digital age. The adoption of developmentally appropriate practices using AI-enabled techniques for facilitating the performance of teaching and learning in the higher education domain is thus a necessary task, especially in the COVID 19 pandemic era. The development and implementation of such techniques involve many factors and are related to the classical multiple criteria decision-making (MCDM) issue; however, these factors surrounding supervisors will confuse them and may result in misjudgment. To clarify the relevant issues and illustrate the cause-and-effect relationships among factors, a hybrid soft-computing technique (i.e., the fuzzy rough set theory (FRST) with ant colony optimization (ACO)) and a DEMATEL approach was proposed in this study, which can help decision makers capture the best model necessary for achieving aspiration-level in a higher education management strategy. In the results submitted, the improvement priority for dimensions is based on the measurement of the influences, running in order of tutors for learners (A), skills and competences (B), interaction data to support learning (C), and universal access to global classrooms (D), and which can serve as a reference for the plan of AI-enabled teaching/learning for higher education.

A Novel Unsupervised Approach to Heterogeneous Feature Selection Based on Fuzzy Mutual Information

Aiming at the problem of effectively selecting relevant features from heterogeneous data without decision, a novel feature selection approach is studied based on fuzzy mutual information in fuzzy rough set theory. First, the fuzzy relevance of each feature is defined by using fuzzy mutual information, and then, the fuzzy conditional relevance is further given. Next, the fuzzy redundancy is defined by using the difference between the fuzzy relevance and the fuzzy conditional relevance. Thereby, the evaluation index of the feature importance is obtained by using the idea of unsupervised minimum redundancy and maximum relevance. Finally, a fuzzy-mutual-information-based unsupervised feature selection algorithm is designed to select feature sequences. Extensive experiments are conducted on public datasets, and six unsupervised feature selection algorithms are compared. The selected features are evaluated by classification, clustering, and outlier detection methods. Experimental results show that the proposed algorithm can select fewer heterogeneous features to maintain or improve the performance of learning algorithms.

Situation Element Extraction Based on Fuzzy Rough Set and Combination Classifier.

Generalized network security situation awareness technology is divided into three processes: situation element extraction, situation understanding, and situation prediction. Situation element extraction is the most critical step in the whole process, and its extraction quality will directly affect the accuracy of situation understanding and prediction. In view of the shortcomings of current situation element extraction methods, this study makes an in-depth study on the network security situation element extraction algorithm and proposes a situation element extraction model based on the fuzzy rough set and combined classifier, which is used to improve the accuracy of situation elements acquisition, so as to provide a better data basis for situation understanding and prediction. In this study, the theory of fuzzy rough set is used to reduce the attributes of data without reducing the ability of data classification, which reduces the complexity of data; using the combination classifier theory and particle swarm optimization algorithm, a framework of situation element extraction is built, which can extract situation elements more accurately. The experimental results show that the network security situation element extraction framework proposed in this study can effectively shorten the extraction time of situation elements and improve the accuracy of situation element acquisition under the premise of ensuring the ability of data classification, thus proving the effectiveness and feasibility of the situation element extraction framework proposed in this study.

Fuzzy-rough hybrid dimensionality reduction

Dimensionality reduction including feature selection and feature extraction is a significant preprocessing method for data analysis, which is an important application of fuzzy rough set theory. Linear discriminant analysis (LDA) is a commonly used supervised feature extraction method, which can generate transformations while retaining as much class discrimination information as possible. However, it is worth noting that linear discriminant analysis is not interpretable. To improve the interpretability of the model and avoid losing part of the original feature information when only using feature selection for dimensionality reduction, this paper proposes a hybrid dimensionality reduction method based on fuzzy rough set and linear discriminant analysis. It can obtain a reduction set that contains complementary transformation features and original features. First, the semi-feature set is generated by criterion based on the normalized fuzzy joint mutual information, and the hybrid feature set is further induced by applying LDA to the feature set. Then, the redundancy between features is evaluated by the normalized fuzzy mutual information. The significance of a feature is defined by the proposed normalized effective classification information amount and the symmetric effective classification information amount. Next, the priority value between features according to the significance of them is defined to delete the redundant feature from the hybrid feature set. Furthermore, a hybrid dimensionality reduction algorithm based on fuzzy rough set is designed further. Finally, the performance of the proposed method is compared with some methods. The experimental results show that the proposed algorithm can obtain effective feature subset, which improve the performance of a classifier.

Student-t kernelized fuzzy rough set model with fuzzy divergence for feature selection

Fuzzy rough set theory can tackle feature redundancy in data and select more informative features for machine learning tasks. Gaussian kernel is often coupled with fuzzy rough set theory to measure fuzzy relation between data instances. However, Gaussian kernel has a serious long-tail phenomenon, which would perform poorly in modeling the fuzzy relation for high-dimensional data. Moreover, a robust feature evaluation function is also nontrivial in a fuzzy rough set model because a naive model may select those non-optimal feature subsets due to the perturbations from redundant features. This paper delves into Student-t kernel and fuzzy divergence to address these challenges for fuzzy rough feature selection. This paper proposes a new Student-t Kernelized Fuzzy Rough Set (SKFRS) model. The new model uses fuzzy divergence to evaluate uncertain information in the data. It also explores a newly-defined feature evaluation function on the biases of the dynamic relation between the relevance and indispensability of features in feature selection process. A novel forward greedy search algorithm is then presented to solve the final objective function. The selected features are subsequently evaluated on downstream classification tasks. Experimental results using real-world datasets demonstrate the effectiveness of the proposed model and its superiority against the baseline methods.

Real-valued hemimetric-based fuzzy rough sets and an application to contour extraction of digital surfaces

Binary relations, coverings and neighborhood systems/operators are useful tools to study fuzzy rough set theory. In this paper, we use the notion of real-valued hemimetric, a weak version of the standard metric, as the basic structure to define and study fuzzy rough sets by using the usual addition and subtraction of real numbers. We define a pair of fuzzy upper and lower rough approximation operators and investigate their properties and interrelations. These two operators have nice logical descriptions by using the Lukasiewicz logical system. It is shown that upper definable fuzzy subsets, lower definable fuzzy subsets and Lipschitz fuzzy subsets are the same thing in this model. Definable fuzzy subsets are exactly the upper sets with respect to the induced fuzzy preorder, which form a stratified Alexandrov fuzzy topology. A comparison between hemimetric-based fuzzy rough sets and fuzzy preorder-based fuzzy rough sets has been made. Results show that the former can be considered as a real-valued extension of the latter. At the end, an application of the hemimetric-based rough set model to contour extraction of digital surfaces is proposed.

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.

Multi-attribute predictive analysis based on attribute-oriented fuzzy rough sets in fuzzy information systems

Multi-attribute decision making (MADM) plays an important role in decision analysis. Based on a new fuzzy rough set theory (FRS), this paper presents a multi-attribute prediction analysis model in fuzzy information systems (FISs). In this prediction model, the proposed FRS is based on an attribute-oriented fuzzy similarity relation; the cosine deviation of a candidate to optimistic decision and pessimistic decision is proposed to construct a trend function, for further predicting the development trend of the candidate. It deals with MADM problems from the perspective of multi-attribute predictive analysis, and is a valuable continuation of fuzzy decision making research. To evaluate the validity and feasibility of the proposed prediction model, experiments with real data sets and comparative experimental analysis are conducted. The experimental results prove that the prediction performance of the proposed model is well-pleasing in terms of both prediction accuracy and AUC results.

Predictive Maintenance Model Based on Multisensor Data Fusion of Hybrid Fuzzy Rough Set Theory Feature Selection and Stacked Ensemble for Fault Classification

With the rising demand for integrated and autonomous systems in the field of engineering, efficient frameworks for instant detection of performance anomalies are imperative for improved productivity and cost-effectiveness. This study proposes a systematic predictive maintenance framework based on the hybrid multisensor fusion technique of fuzzy rough set feature selection and stacked ensemble for the efficient classification of fault conditions characterised by uncertainties. First, a feature vector of time-domain features was extracted from 17 multiple sensor signals. Then, a comparative study of six different Fuzzy Rough Set Feature Selection (FRFS) methods was employed to select the various combinations of optimal feature subsets for various faults classification tasks. The determined optimal feature subsets then served as inputs for training the stacked ensemble (ESB(STK)). In the ESB(STK), Support Vector Machine (SVM), Multilayer Perceptron (MLP), k -Nearest Neighbour ( k -NN), C4.5 Decision Tree (C4.5 DT), Logistic Regression (LR), and Linear Discriminant Analysis (LDA) served as the base classifiers while the LR was selected to be the metaclassifier. The proposed hybrid framework (FRFS-ESB(STK)) improved the classification accuracy with the selected combinations of optimal feature subset size whiles reducing the computational cost, overfitting, training runtime, and uncertainty in modelling. Overall analyses showed that the FRFS-ESB(STK) proved to be generalisable and versatile in the classification of all conditions of four monitored hydraulic components (i.e., cooler, valve, accumulator, and internal pump leakage) when compared with the six base classifiers (standalone) and three existing ensemble classifiers (Stochastic Gradient Boosting (SGB), Ada Boost (ADB), and Bagging (BAG)). The proposed FRFS-ESB(STK) showed an average improvement of 11.28% and 0.88% test accuracies when classifying accumulator and pump conditions, respectively, whiles 100% classification rates were obtained for both cooler and valve.

Bioretention Systems Optimization and Design Characterization Model Using Fuzzy Rough Set Theory

Urban stormwater has become a persistent concern on a global scale due to its adverse environmental implications. It is the prime vector of aquatic contaminants worldwide that causes pollutants when water bodies drain. Bioretention systems are increasingly used to alleviate setbacks associated with stormwater run-off in urban locales. It has played a substantial role in the implementation of low impact development (LID), a concept that addresses urban stormwater problems caused by land changes and development. The use of LID technologies is an innovative approach. However, it is beset with challenges, such as the insufficiency of data on rainfall distribution and difficulty in interpreting data. To address these research gaps, the present study developed a fuzzy rough set data algorithm for bioretention systems. Event mean concentration calculations and fuzzification of rainfall were performed to produce a rough set-based decision rule. Using the Weibull probability distribution, fuzzification of rainfall and parameter data, rule induction, and Preece testing, bioretention design considerations were determined. The bioretention characterizations generated evident pollutants present in the catch basin before and after filtration. In addition, the bioretention characterization conducted in this study was able to reduce the number of tests needed for rainfall identification based on the different attributes.

Exploring the mutual influence among the social innovation factors amid the COVID-19 pandemic

From the triple bottom line, the social aspect has received relatively limited attention during the Corona Virus Disease (COVID-19) pandemic, particularly in the emerging economies. Social innovation factors help improve the sustainability performance of the companies. This study develops a social innovation decision framework and analyses the interrelationships among social innovation factors considering the COVID-19 situation. For this purpose, the Decision-Making Trial and Evaluation Laboratory (DEMATEL) is extended by integrating the Z numbers and rough fuzzy set theory into its computational procedure. Z-numbers address the uncertainty of the decision and experts’ confidence in the evaluation and rough numbers are used for aggregating the experts’ opinions. On this basis, the mutual influence of social innovation factors and the influence weights of these factors are investigated. The results suggest that a quick response to market demand for sustainable products is the most influential factor in attaining social sustainability innovation during the pandemic. This article is concluded by providing insights for industrial experts and decision-makers to understand the underpinnings of social sustainability innovation during unforeseen situations.

Fast Detection of Diarrhetic Shellfish Poisoning Toxins in Mussels Using NIR Spectroscopy and Improved Twin Support Vector Machines

Diarrhetic shellfish poisoning (DSP) toxins are potent marine biotoxins. It can cause a severe gastrointestinal illness by the consumption of mussels contaminated by DSP toxins. New methods for effectively and rapidly detecting DSP toxins-contaminated mussels are required. In this study, we used near-infrared (NIR) reflection spectroscopy combined with pattern recognition methods to detect DSP toxins. In the range of 950-1700 nm, the spectral data of healthy mussels and DSP toxins-contaminated mussels were acquired. To select optimal waveband subsets, a waveband selection algorithm with a Gaussian membership function based on fuzzy rough set theory was applied. Considering that detecting DSP toxins-contaminated mussels from healthy mussels was an imbalanced classification problem, an improved approach of twin support vector machines (TWSVM) was explored, which is based on a centered kernel alignment. The influences of parameters of the waveband selection algorithm and regularization hyperparameters of the improved TWSVM (ITWSVM) on the performance of models were analyzed. Compared to conventional SVM, TWSVM, and other state-of-the-art algorithms (such as multi-layer perceptron, extreme gradient boosting and adaptive boosting), our proposed model exhibited better performance in detecting DSP toxins and was little affected by the imbalance ratio. For the proposed model, the F-measure reached 0.9886, and detection accuracy reached 98.83%. We explored the physical basis for the detection model by analyzing the relationship between the occurrence of overtone and combination bands and selected wavebands. This study supports NIR spectroscopy as an innovative, rapid, and convenient analytical method to detect DSP toxins in mussels.

A noise-aware fuzzy rough set approach for feature selection

Feature selection has aroused extensive attention and aims at selecting features that are highly relevant to classification from raw datasets to improve the performance of a learning model. Fuzzy rough set theory is a powerful mathematical method for feature selection. The classical fuzzy rough set model is very sensitive to the noise while the noise samples in classification data often appear. In addition, fuzzy rough set theory does not fit well when the density distribution of the samples in the dataset varies greatly. Thus, it is of great significance to improve the robustness of fuzzy rough set models and its adaptability to data for feature selection. Inspired by these issues, we focus on the robust fuzzy rough set approach for feature selection. We first propose a robust fuzzy rough set model based on data distribution to achieve the purpose of anti-noise i.e., Noise-aware Fuzzy Rough Sets (NFRS) model. This model proposes a novel search mechanism, which weakens the sensitivity of the approximation operator to noise by considering the distribution of samples in the decision classes to weight the samples, further obtains three kinds of samples, i.e., intra-class samples, boundary samples, and outlier samples. Then, the degrees of relevance of the feature for class is defined by the dependency function based on the NFRS model to evaluate the significance of the feature subset. On this basis, an evaluation function about feature significance is constructed, which simultaneously considers the relevance and redundancy of a candidate feature provided for the selected subset and the remaining feature subset. A novel forward greedy search algorithm is presented to select a feature sequence. The selected features are subsequently evaluated with downstream classification tasks. Experimental using real-world datasets demonstrate the effectiveness of the proposed model and its superiority against comparison baseline methods.

Weighted fuzzy rough sets-based tri-training and its application to medical diagnosis

The theory of fuzzy rough sets is an effective soft computing paradigm for dealing with vague, uncertain, or imprecise data. However, most existing fuzzy rough sets-based methods may suffer from robustness since all samples are considered equally and also these methods are designed to cater for supervised or unsupervised learning. In this paper, we propose a weighted fuzzy rough sets-based multi-view tri-training model for partially labeled data. Specifically, considering the negative effect of noise, we first use a technique of data editing to filter potentially possible noises, and then a gradient descent algorithm is employed to optimize the weight of each sample with the objective of maximizing high-order weighted fuzzy dependency, based on which a robust weighted fuzzy rough set model is developed for labeled data. Moreover, we introduce the robust weighted fuzzy rough sets into tri-training and propose multi-view-based robust tri-training for partially labeled data by exploring data representations in the original view, the transformed view of principal component analysis, and the granular view after discretization. Extensive experiments conducted on UCI benchmark and medical diagnosis data sets show that the proposed model achieves favorable results in both supervised and semi-supervised scenarios.

Exploring interactive attribute reduction via fuzzy complementary entropy for unlabeled mixed data

Attribute reduction is one of the important applications in fuzzy rough set theory. However, most attribute reduction methods in fuzzy rough theory mainly focus on removing irrelevant or redundant attributes. There are few reports about the method of considering attribute interaction. For this reason, this paper proposes an interactive attribute reduction method for unlabeled mixed data. First, some uncertainty measures based on fuzzy complementary entropy are further defined. Then, based on the proposed uncertainty measure, the attribute evaluation criteria of maximal information, minimal redundancy, and maximal interactivity are developed respectively. As a result, the evaluation index of the attribute importance is established by using the idea of unsupervised maximal information-minimal redundancy-maximal interactivity. Finally, a corresponding algorithm is designed to select attributes. The experimental results show that the proposed algorithm has better performance.