Classical Rough Set Research Articles

Sequential rough set: a conservative extension of Pawlak’s classical rough set

Rough set theory is an important approach to deal with uncertainty in data mining. However, Pawlak’s classical rough set has low fault-tolerance on concept approximation based on knowledge granules, which may influence the classification accuracy in practical application. To address this problem, the present paper proposes a novel sequential rough-set model that is proved to be a conservative extension of Pawlak’s classical rough set. As a result, it effectively improves the fault-tolerance ability, classification accuracy and concept approximation accuracy of the latter without any additional assumption. Based on the properties and theoretical analysis of the proposed model, an algorithm is presented to automatically determine the sequential thresholds and compute the three regions for the given concept. Experiments on real data verify the validity of the algorithm, and also show the stable improvement on the two types of accuracy.

Retraction Note: Covering-based rough set classification system

Retraction Note: Covering-based rough set classification system

Double-local conditional probability based fast calculation method for approximation regions of local rough sets

As an important extension of classical rough sets, local rough set model can effectively process data with noise. How to effectively calculate three approximation regions, namely positive region, negative region and boundary region, is a crucial issue of local rough sets. Existing calculation methods for approximation regions are based on conditional probability, the time complexity is O (|X||U||C|). In order to improve the computational efficiency of three approximation regions of local rough sets, we propose a double-local conditional probability based fast calculation method. First, to improve the computational efficiency of equivalence class, we define the double-local equivalence class. Second, based on the double-local equivalence class, we define the double-local conditional probability. Finally, given the probability thresholds and a local equivalence class, the monotonicity of double-local conditional probability is proved, on this basis, a double-local conditional probability based fast calculation method for approximation regions of local rough sets is proposed, and the time complexity is O (MAX (|X|2|C|, |X||XC||C|)). Experimental results based on 9 datasets from UCI demonstrate the effectiveness of the proposed method.

Optimization Analysis of the Path of Ideological and Political Construction in Higher Vocational English Courses Based on Intelligent Data Analysis

Abstract Incorporating the elements of curriculum Ideological and Politics in English teaching is an important way to enhance the effect of nurturing, and this paper explores its integration. In the paper, the intelligent data mining process for the construction of higher vocational English curriculum Ideological and Politics is constructed, and the related data are integrated based on the rough set method to explore the set relationship between the construction of intelligent data. In addition, combined with the PSO algorithm, the PSOBR algorithm is constructed on the basis of the PSORSFS algorithm of PSO’s rough set feature selection for the optimization of the path of construction of the English curriculum Ideological Politics. On this basis, relevant data on English majors in higher vocational colleges and universities were collected to carry out empirical research on the path of Ideological and Political construction of English courses in higher vocational colleges and universities. The results show that the main distribution of GPA of the three groups of students based on rough set classification is (0.60,0.80), (0.36,0.50), (0.24,0.44), respectively, and the distribution of the construction of higher vocational English courses is not balanced. The average construction effect after optimization has been improved by 0.30, and the highest construction effect has been improved by 0.42, which makes the optimization effect obvious. The optimization effect of the path of English course ideological and political construction through the formation of a professional teaching team, enrichment of teaching methods, and other means is obvious.

An Application on an Information System via Nano Ordered Topology

Rough set theory is commonly used to handle uncertainty in various applications. In order to broaden its application scope, the classical rough set model based on equivalence relations, it has been extended to include an additional partial order relation. This partial order relation represents an m-nano flou set, as defined in Section 5, between rough sets and is particularly useful in determining the levels of impact that key factors have on heart failure. The primary objective of the current research is to introduce a novel approximation method based on equivalence relations and partial order relations (ordered approximation spaces), which extends Pawlak's method and investigates related results. The paper establishes the equivalence between our approach and Pawlak's approach under the condition that we have an equivalence relation and a partial order relation that satisfies the criteria required for it to be considered an equality relation. The second objective is to extend the concept of nano topology to include nano ordered topology, which involves nano increasing or decreasing topological spaces. The research indicates that incorporating nano increasing or decreasing topological spaces results in enhanced data analysis accuracy when compared to solely utilizing nano topological spaces. This observation aligns with the discussions in the referenced work by Jayalakshmi. The findings of this research have the potential to significantly impact medical research related to heart failure. Improved methods for handling uncertainty and quantifying the influence of various factors can lead to more accurate and reliable predictions and diagnoses. Ultimately, this work aims to contribute to advancements in heart failure treatment and prevention. By bridging the gap between traditional rough set theory and the nuanced intricacies of heart failure analysis, our research strives to advance our comprehension of this critical medical condition and, in turn, support progress in heart failure treatment and prevention.

Fuzzy rough sets based on fuzzy quantification

Classical (fuzzy) rough sets exhibit sensitivity to noise, which is particularly undesirable for machine learning applications. One approach to solve this issue is by making use of fuzzy quantifiers, as done by the vaguely quantified fuzzy rough set (VQFRS) model. While this idea is intuitive, the VQFRS model suffers from both theoretical flaws as well as from suboptimal performance in applications. In this paper, we improve on VQFRS by introducing fuzzy quantifier-based fuzzy rough sets (FQFRS), which proposes an intuitive fuzzy rough approximation operator that utilizes general unary and binary quantification models. We show how several existing models fit inside FQFRS, as well as how it inspires novel ones. Additionally, we propose several binary quantification models to be used with FQFRS. Furthermore, we conduct a theoretical study of their properties, and investigate their potential by applying them to classification problems. In particular, we highlight the effectiveness of Yager's Weighted Implication-based (YWI) binary quantification model, which induces a fuzzy rough set model that is both a significant improvement on VQFRS, as well as a worthy competitor to the popular ordered weighted averaging based fuzzy rough set (OWAFRS) model.

Optimal scale selection and knowledge discovery in generalized multi-scale decision tables

In the real world, each attribute of data sets has multiple scales, whether it is a conditional attribute or a decision attribute. Knowledge mined from data based on the optimal scale can well meet the needs of real life. Hence, there is no denying that optimal scale selection is an problem to be solved urgently in the knowledge discovery field of multi-scale decision tables. The optimal scale combines coarser condition attributes with the finer decision attribute, so as to achieve a balance between efficiency and accuracy. With the aim of selecting the optimal scale combination, we firstly explore some related properties and theorems of generalized multi-scale decision tables. Then we define the optimal scale in generalized multi-scale decision tables and propose two algorithms for optimal scale selection. In addition, a knowledge acquisition algorithm and a multi-scale rough set classifier framework are proposed. Finally, numerical experiments are performed on some open data sets to test the effectiveness of the algorithms.

An interval rough number variable precision rough sets model and its attribute reduction

The interval rough number rough sets model is the generalization of the classical rough sets. Since the lower approximation condition of interval rough number rough sets model is a full inclusion relation which is too strict to tolerate noisy data, strict conditions increase the possibility of a sample classified into a wrong class. To overcome the above shortcomings, an interval rough number variable precision rough sets model is proposed in this paper, which is combined with interval rough number similarity and the concept of variable precision rough sets. The model introduces the error parameter and can improve the tolerance of noise data. Then the related properties of the model are also proved. Moreover, we construct a maximal positive domain attribute reduction method based on the proposed model, which can process the data type of interval rough number without discretization. Finally, numerical examples are given to verify the rationality of the model.

Feature selection for multiset-valued data based on fuzzy conditional information entropy using iterative model and matrix operation

Multiset-valued data is a powerful tool to deal with missing feature values. Classical rough set theory is sensitive to noise in classification learning due to the stringent condition of equivalence relation. Thus, a class of fuzzy relations can be introduced to describe the similarity between samples in multiset-valued data. However, these fuzzy relations have deficiencies when they are used in the computation of fuzzy conditional information entropy. This paper proposes a new model for multiset-valued data by introducing two variable parameters: one controls the similarity between samples, the other dominates the distance between feature values. This model employs the iterative computation strategy to define fuzzy conditional information entropy that is computing by matrix. The notions of three fuzzy information entropies in a multiset-valued decision information system (MVDIS) are put forward. For measuring any added feature, the significance based on fuzzy conditional information entropy is introduced. Moreover, fuzzy conditional information entropy iterative model (FCIEI-model) is presented. Finally, feature selection in an MVDIS based on FCIEI-model and matrix operation is researched, and the relevant algorithm (denoted as FCIEIM-MO algorithm) is proposed. The experimental results demonstrate that FCIEIM-MO algorithm possesses good robustness and is superior to some feature selection algorithms. The experimental results demonstrate that FCIEIM-MO algorithm possesses good robustness and exhibit better performance compared with some feature selection algorithms.

A Rough Set Framework for Multihuman Tracking in Surveillance Video

Multi-human tracking has become a key focus area in video surveillance applications. Several research works have been carried out in multi-human tracking in the past two decades. The techniques such as kalman filter, particle filter, markov chain process, blob detection, etc., have been used to detect and track humans. However, tracking the human objects in consecutive frames is still a challenging problem due to spatial disorder, non-linear motion and occlusion of human objects. Also, the human object labeling becomes difficult since most of the similarity measures used in the classification process do not consider the positional coordinates while computing the similarity. This paper addresses the above challenges by introducing a rough set framework which identifies the human objects using modified bounding box generation technique and by applying the rough set classifier. The framework was tested on the benchmark dataset PETS09 and the experimental results were compared with OCELM, MODT and MPTS algorithms. The comparative analysis shows that the rough set framework outperforms the existing algorithms in terms of detection and tracking accuracy even in the cases of overlapped and hidden human objects.

Attribute Reduction for Information Systems via Strength of Rules and Similarity Matrix

An information system is a type of knowledge representation, and attribute reduction is crucial in big data, machine learning, data mining, and intelligent systems. There are several ways for solving attribute reduction problems, but they all require a common categorization. The selection of features in most scientific studies is a challenge for the researcher. When working with huge datasets, selecting all available attributes is not an option because it frequently complicates the study and decreases performance. On the other side, neglecting some attributes might jeopardize data accuracy. In this case, rough set theory provides a useful approach for identifying superfluous attributes that may be ignored without sacrificing any significant information; nonetheless, investigating all available combinations of attributes will result in some problems. Furthermore, because attribute reduction is primarily a mathematical issue, technical progress in reduction is dependent on the advancement of mathematical models. Because the focus of this study is on the mathematical side of attribute reduction, we propose some methods to make a reduction for information systems according to classical rough set theory, the strength of rules and similarity matrix, we applied our proposed methods to several examples and calculate the reduction for each case. These methods expand the options of attribute reductions for researchers.

Information-theoretic partially labeled heterogeneous feature selection based on neighborhood rough sets

With the rapid increase of large-scale, real-world datasets, it becomes critical to address the problem of partially labeled heterogeneous feature selection (i.e., some samples, which own numerical and categorical features, have no labels). Existing solutions typically adopt linear correlations between features. In this paper, three different monotonic uncertainty measures are defined on equivalence classes and neighborhood classes to study the partially labeled heterogeneous feature selection by exploring the nonlinear correlations. First, consistent entropy and monotonic neighborhood entropy, based on classical rough set theory and neighborhood rough set theory, are proposed to construct a uniform measure for feature selection in heterogeneous datasets. Furthermore, a maximal neighborhood entropy strategy is developed by considering the inconsistency of neighborhood classes described by the features and partial labels. Finally, two feature selection algorithms are presented by three novel monotonic uncertainty measures. The comparative experiments demonstrate the effectiveness and superiority of the newly proposed feature selection measures.

A New Rough Set Classifier for Numerical Data Based on Reflexive and Antisymmetric Relations

The grade-added rough set (GRS) approach is an extension of the rough set theory proposed by Pawlak to deal with numerical data. However, the GRS has problems with overtraining, unclassified and unnatural results. In this study, we propose a new approach called the directional neighborhood rough set (DNRS) approach to solve the problems of the GRS. The information granules in the DNRS are based on reflexive and antisymmetric relations. Following these relations, new lower and upper approximations are defined. Based on these definitions, we developed a classifier with a three-step algorithm, including DN-lower approximation classification, DN-upper approximation classification, and exceptional processing. Three experiments were conducted using the University of California Irvine (UCI)’s machine learning dataset to demonstrate the effect of each step in the DNRS model, overcoming the problems of the GRS, and achieving more accurate classifiers. The results showed that when the number of dimensions is reduced and both the lower and upper approximation algorithms are used, the DNRS model is more efficient than when the number of dimensions is large. Additionally, it was shown that the DNRS solves the problems of the GRS and the DNRS model is as accurate as existing classifiers.

Pruning Decision Rules by Reduct-Based Weighting and Ranking of Features.

Methods and techniques of feature selection support expert domain knowledge in the search for attributes, which are the most important for a task. These approaches can also be used in the process of closer tailoring of the obtained solutions when dimensionality reduction is aimed not only at variables but also at learners. The paper reports on research where attribute rankings were employed to filter induced decision rules. The rankings were constructed through the proposed weighting factor based on the concept of decision reducts-a feature reduction mechanism embedded in the rough set theory. Classical rough sets operate only in discrete input space by indiscernibility relation. Replacing it with dominance enables processing real-valued data. Decision reducts were found for both numeric and discrete attributes, transformed by selected discretisation approaches. The calculated ranking scores were used to control the selection of decision rules. The performance of the resulting rule classifiers was observed for the entire range of rejected variables, for decision rules with conditions on continuous values, discretised conditions, and also inferred from discrete data. The predictive powers were analysed and compared to detect existing trends. The experiments show that for all variants of the rule sets, not only was dimensionality reduction possible, but also predictions were improved, which validated the proposed methodology.

Variable precision multi-granulation composite rough sets with multi-decision and their applications to medical diagnosis

Rough set theory has become an effective tool to address uncertain decision-making problems. Nevertheless, existing rough set-based decision-making methods cannot effectively deal with the management decision-making problems with heterogeneity, multi-decision, and diversified attributes simultaneously. Given this, the purpose of this paper is to explore an effective classification solution for solving decision-making problems with the above-described characteristics from the perspective of granular computing. First, we present the notion of heterogeneous diversified attribute multi-decision systems. Because attribute semantics is crucial to multi-attribute decision analysis, we then divide an attribute set into nine subsets according to attribute semantics. Further, a composite binary relation that fits the realistic attribute features is constructed. Subsequently, considering different decision scenarios, we establish four kinds of variable precision multi-decision multi-granulation rough set models. Meanwhile, the related properties and relationships of these models are explored. We find that the established models are extensions of the existing classical rough sets. In the end, we apply the established models to an illustrative example of medical diagnosis. The results of the case and comparative analyses demonstrate the models’ feasibility, effectiveness, and superiority. As a result, our work provides a kind of new decision thinking with reasonable semantic analysis for solving complex management decision-making problems in reality.

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.

A parallel rule-based approach to compute rough approximations of dominance based rough set theory

In many datasets, conditional attributes and decision classes are preference-ordered, however, the classical Rough Set Theory (RST) does not consider the preference order between the values of the attributes. An extension of RST known as a Dominance-based Rough Set Approach (DRSA) provides dominance relation in this regard. In DRSA, data analysis mainly depends on the calculations of lower and upper approximations and these two measures are computationally utilizing many resources i.e., time and memory, due to the consideration of preference order. In this paper, we have proposed a parallel technique for calculating DRSA approximation sets. The proposed method directly computes approximations by following heuristic rules without calculating dominance positive or negative relations. The proposed parallel approach is then compared with the conventional method of calculation of DRSA approximations and a recent another technique of parallel processing using ten UCI publicly available datasets. Results validated the efficiency and effectiveness of the proposed model. An average reduction of 83% was observed in execution time and 86% in memory consumption. The structural complexity of the algorithm also considerably reduced.

Outlier Detection Based on Fuzzy Rough Granules in Mixed Attribute Data

Outlier detection is one of the most important research directions in data mining. However, most of the current research focuses on outlier detection for categorical or numerical attribute data. There are few studies on the outlier detection of mixed attribute data. In this article, we introduce fuzzy rough sets (FRSs) to deal with the problem of outlier detection in mixed attribute data. Since the outlier detection model of the classical rough set is only applicable to the categorical attribute data, we use FRS to generalize the outlier detection model and construct a generalized outlier detection model based on fuzzy rough granules. First, the granule outlier degree (GOD) is defined to characterize the outlier degree of fuzzy rough granules by employing the fuzzy approximation accuracy. Then, the outlier factor based on fuzzy rough granules is constructed by integrating the GOD and the corresponding weights to characterize the outlier degree of objects. Furthermore, the corresponding fuzzy rough granules-based outlier detection (FRGOD) algorithm is designed. The effectiveness of the FRGOD algorithm is evaluated through experiments on 16 real-world datasets. The experimental results show that the algorithm is more flexible for detecting outliers and is suitable for numerical, categorical, and mixed attribute data.

Boundary region-based variable precision covering rough set models

As an essential way of knowledge representation and knowledge acquisition in uncertainty theory, variable precision rough set (VPRS) has been widely considered by researchers. Firstly, the corresponding CVPRS model via boundary region is investigated based on an existing covering-based rough set model. Its algebraic structures and properties are systematically studied. This model mainly depicts a pair of boundary operators and a pair of approximation operators with a certain threshold from the perspective of single knowledge granularity. And it not only relaxes the complete inclusion relation but also retains the basic properties of the classical rough set. Secondly, an attribute reduction approach is given for a covering-based decision information systemusing the proposed CVPRS model, which keeps the lower or upper approximation unchanged. The different performances of boundary operators and their related three indices in these reduction methods are compared. The results show that boundary operators and distribution functions have outstanding advantages in these applications. Finally, an extraction method of necessity rules and possibility rules corresponding to decision classes are established. The validity and security of the above methods are verified theoretically. Numerical experiments further show that the proposed models and methods have a certain application value.

Data Mining-Based Cyber-Physical Attack Detection Tool for Attack-Resilient Adaptive Protective Relays

Maintaining proper operation of adaptive protection schemes is one of the main challenges that must be considered for smart grid deployment. The use of reliable cyber detection and protection systems boosts the preparedness potential of the network as required by National Infrastructure Protection Plans (NIPPS). In an effort to enhance grid cyber-physical resilience, this paper proposes a tool to enable attack detection in protective relays to tackle the problem of compromising their online settings by cyber attackers. Implementing the tool first involves an offline phase in which Monte Carlo simulation is used to generate a training dataset. Using rough set classification, a set of If-Then rules is obtained for each relay and loaded to the relays at the initialization stage. The second phase occurs during online operation, with each updated setting checked by the corresponding relay’s built-in tool to determine whether the settings received are genuine or compromised. A test dataset was generated to assess tool performance using the modified IEEE 34-bus test feeder. Several assessment measures have been used for performance evaluation and their results demonstrate the tool’s superior ability to classify settings efficiently using physical properties only.