Concepts Of Rough Set Theory Research Articles

Roughness Established on A Set-Valued Homomorphism

This paper aims to study and apply some concepts of rough set theory (upper and lower approximations) on a set-valued homomorphism which is induced by a soft semiring homomorphism similarity as on a ring homomorphism. Furthermore, our findings are considered as a novel in the T-rough group and ideals that had been studied.

An improved rough set strategy-based sine cosine algorithm for engineering optimization problems

In this paper, a hybrid algorithm called rough sine cosine algorithm (RSCA) is introduced for solving engineering optimization problems by merging the sine cosine algorithm (SCA) with the rough set theory concepts (RST). RSCA combines the benefits of SCA and RST to focus the search for a promising region where the global solution can be found. Due to imprecise information on the optimization problems, efficient algorithms roughly identify the optimal solution for this type of uncertain data. The fundamental motive for adding the RST is to deal with the imprecision and roughness of the available information regarding the global optimal, especially for large dimensional problems. The cut concept of RST targeted the more interesting search region so the optimal operation could be sped up, and the global optimum could be reached at a low computational cost. The proposed RSCA algorithm is tested on 23 benchmark functions and 3 design problems. RSCA’s obtained results are mainly compared to the SCA, which is used as a first level of the proposed algorithm in this work and those of other algorithms in the literature. According to the comparisons, the RSCA can provide very competitive performance with different algorithms.

Fixed Point Results in Rough Metric Spaces

In the present paper, we prove some fixed point results in Rough metric spaces. Rough set theory has a significant importance in many fields. The aim of this paper is to describe some properties of rough sets. Moreover, we give further study on Pawlak rough sets and introduce new examples some rough set theory concepts.

ENTROPY BASED GREEDY UNSUPERVISED FEATURE SELECTION METHOD USING ROUGH SET THEORY FOR CLASSIFICATION

Feature selection technique attempts to select and remove irrelevant features while ensuring that an informative subset of features remains in the dataset. The performance of a classifier often depends on the feature subset used for the robust classification task. In the medical and healthcare application domain, classification accuracy plays a vital role. The higher level of false negatives in medical diagnosis systems may raise the risk of patients not employing the necessary treatment they need. In this article, we have proposed an unsupervised feature selection method that underlines the concepts of rough set theory for the task of classification of high-dimensional datasets. Experiments are carried out on seven public domain healthcare and life science related datasets. The obtained experimental results justify the significance of the proposed method over five other state-of-the-art feature selection methods.

Maximal rough neighborhoods with a medical application.

In this paper, we focus on the main concepts of rough set theory induced from the idea of neighborhoods. First, we put forward new types of maximal neighborhoods (briefly, {mathcal {M}}_{sigma} -neighborhoods) and explore master properties. We also reveal their relationships with foregoing neighborhoods and specify the sufficient conditions to obtain some equivalences. Then, we apply {mathcal {M}}_{sigma} -neighborhoods to define {mathcal {M}}_{sigma} -lower and {mathcal {M}}_{sigma} -upper approximations and elucidate which one of Pawlak’s properties are preserved (evaporated) by these approximations. Moreover, we research {mathcal {A}}_{Msigma }-accuracy measures and prove that they keep the monotonic property under any arbitrary relation. We provide some comparisons that illustrate the best approximations and accuracy measures are obtained when sigma =langle irangle . To show the importance of {mathcal {M}}_{sigma} -neighborhoods, we present a medical application of them in classifying individuals of a specific facility in terms of their infection with COVID-19. Finally, we scrutinize the strengths and limitations of the followed technique in this manuscript compared with the previous ones.

Rough set models in a more general manner with applications

<abstract><p>Several tools have been put forth to handle the problem of uncertain knowledge. Pawlak (1982) initiated the concept of rough set theory, which is a completely new tool for solving imprecision and vagueness (uncertainty). The main notions in this theory are the upper and lower approximations. One of the most important aims of this theory is to reduce the vagueness of a concept to uncertainty areas at their borders by decreasing the upper approximations and increasing the lower approximations. So, the object of this study is to propose four types of approximation spaces in rough set theory utilizing ideals and a new type of neighborhoods called "the intersection of maximal right and left neighborhoods". We investigate the master properties of the proposed approximation spaces and demonstrate that these spaces reduce boundary regions and improve accuracy measures. A comparative study of the present methods and the previous ones is given and shown that the current study is more general and accurate. The importance of the current paper is not only that it is introducing new kinds of approximation spaces relying mainly on ideals and a new type of neighborhoods which increases the accuracy measure and reduces the boundary region of subsets, but also that these approximation spaces are monotonic, which means that it can be successfully used to evaluate the uncertainty in the data. In the end of this paper, we provide a medical example of the heart attacks problem to show the efficiency of the current techniques in terms of approximation operators, accuracy measures, and monotonic property.</p></abstract>

Two dimensional rough online Tesselation automaton and its properties

The concept of rough set theory was introduced in Formal Languages and Automata theory to find Rough Automata, Rough Languages and Rough Grammar. Rough Automata theory can be recognized as an efficient mathematical model in Machine learning and Data mining. In this research article, the rough sets notion is introduced in two dimensional automata theory. Rough set idea is incorporated in Two Dimensional Four Way Finite State Automata and Two Dimensional Online Tesselation Automata to give Two Dimensional Four Way Rough Finite state Automata and Two Dimensional Rough Online Tesselation Automata respectively. The Rough transition map extension of Two Dimensional Rough Online Tesselation Automata is done. The characterizations of Two Dimensional Rough Online Tesselation Automata are studied. Closure properties of Rough Languages recognized by Two Dimensional Rough Online Tesselation Automata under Boolean operations are obtained. Finally the relationship between Two Dimensional Four Way Rough Finite state Automata and Two Dimensional Rough Online Tesselation Automata is established.

Using Rough Set Theory to Find Minimal Log with Rule Generation

Data pre-processing is a major difficulty in the knowledge discovery process, especially feature selection on a large amount of data. In literature, various approaches have been suggested to overcome this difficulty. Unlike most approaches, Rough Set Theory (RST) can discover data de-pendency and reduce the attributes without the need for further information. In RST, the discernibility matrix is the mathematical foundation for computing such reducts. Although it proved its efficiency in feature selection, unfortunately it is computationally expensive on high dimensional data. Algorithm complexity is related to the search of the minimal subset of attributes, which requires computing an exponential number of possible subsets. To overcome this limitation, many RST enhancements have been proposed. Contrary to recent methods, this paper implements RST concepts in an iterated manner using R language. First, the dataset was partitioned into a smaller number of subsets and each subset processed independently to generate its own minimal attribute set. Within the iterations, only minimal elements in the discernibility matrix were considered. Finally, the iterated outputs were compared, and those common among all reducts formed the minimal one (Core attributes). A comparison with another novel proposed algorithm using three benchmark datasets was performed. The proposed approach showed its efficiency in calculating the same minimal attribute sets with less execution time.

A Detailed Study of the Distributed Rough Set Based Locality Sensitive Hashing Feature Selection Technique

In the context of big data, granular computing has recently been implemented by some mathematical tools, especially Rough Set Theory (RST). As a key topic of rough set theory, feature selection has been investigated to adapt the related granular concepts of RST to deal with large amounts of data, leading to the development of the distributed RST version. However, despite of its scalability, the distributed RST version faces a key challenge tied to the partitioning of the feature search space in the distributed environment while guaranteeing data dependency. Therefore, in this manuscript, we propose a new distributed RST version based on Locality Sensitive Hashing (LSH), named LSH-dRST, for big data feature selection. LSH-dRST uses LSH to match similar features into the same bucket and maps the generated buckets into partitions to enable the splitting of the universe in a more efficient way. More precisely, in this paper, we perform a detailed analysis of the performance of LSH-dRST by comparing it to the standard distributed RST version, which is based on a random partitioning of the universe. We demonstrate that our LSH-dRST is scalable when dealing with large amounts of data. We also demonstrate that LSH-dRST ensures the partitioning of the high dimensional feature search space in a more reliable way; hence better preserving data dependency in the distributed environment and ensuring a lower computational cost.

A dynamic approach for updating the optimal approximation of rough set

The approximate representation and calculation of target concept on approximate space are the foundation of rough set model study. For dynamic attribute reduction and related tasks, it is often necessary to update the approximation of the target concept of rough set theory, and most existing updating approaches are based on the lower and upper approximations of target concepts. This paper presents a dynamic approach for updating the optimal set when a single object is added into the decision table. Aiming at the dynamic change of condition class and decision class caused by the incremental object, the paper discusses the updating mechanisms of optimal approximation set in four different cases and then the dynamic updating algorithm of optimal approximation set is obtained. Finally, the experiments on different data sets from UCI show that the time complexity of optimal approximate updating of decision classes are different for four different cases and the incremental methods are feasible and efficient for decision systems of added one single object.

Two dimensional rough online Tesselation automaton and its properties

The concept of rough set theory was introduced in Formal Languages and Automata theory to find Rough Automata, Rough Languages and Rough Grammar. Rough Automata theory can be recognized as an efficient mathematical model in Machine learning and Data mining. In this research article, the rough sets notion is introduced in two dimensional automata theory. Rough set idea is incorporated in Two Dimensional Four Way Finite State Automata and Two Dimensional Online Tesselation Automata to give Two Dimensional Four Way Rough Finite state Automata and Two Dimensional Rough Online Tesselation Automata respectively. The Rough transition map extension of Two Dimensional Rough Online Tesselation Automata is done. The characterizations of Two Dimensional Rough Online Tesselation Automata are studied. Closure properties of Rough Languages recognized by Two Dimensional Rough Online Tesselation Automata under Boolean operations are obtained. Finally the relationship between Two Dimensional Four Way Rough Finite state Automata and Two Dimensional Rough Online Tesselation Automata is established.

A novel fuzzy clustering algorithm based on rough set and inhibitive factor

SummaryAs an important data analysis method, rough set theory can be used to analyze data with uncertainties. Rough set is able to acquire knowledge by the indistinguishable relationship among data objects without any prior knowledge. Rough set theory provides a new theoretical means for solving soft computing problems and has a wide application space in data mining. Meanwhile, the fuzzy C‐means clustering algorithm is sensitive to noisy points and has low convergence speed. In order to deal with the above problems, a novel fuzzy clustering algorithm based on rough set and inhibitive factor is proposed. According to the related concepts of rough set theory, the membership model of fuzzy C‐means algorithm is redefined. Besides, an inhibitive factor is set to improve the convergence speed of the algorithm under the premise of guaranteeing the clustering effect.

Topology in the Alternative Set Theory and Rough Sets via Fuzzy Type Theory

In this paper, we will visit Rough Set Theory and the Alternative Set Theory (AST) and elaborate a few selected concepts of them using the means of higher-order fuzzy logic (this is usually called Fuzzy Type Theory). We will show that the basic notions of rough set theory have already been included in AST. Using fuzzy type theory, we generalize basic concepts of rough set theory and the topological concepts of AST to become the concepts of the fuzzy set theory. We will give mostly syntactic proofs of the main properties and relations among all the considered concepts, thus showing that they are universally valid.

Finding strongly connected components of simple digraphs based on granulation strategy

Strongly connected components (SCCs) are an important kind of subgraphs in digraphs. It can be viewed as a kind of knowledge in the viewpoint of knowledge discovery. In our previous work, a knowledge discovery algorithm called RSCC was proposed for finding SCCs of simple digraphs based on two operators, k-step R-related set and k-step upper approximation, of rough set theory (RST). RSCC algorithm can find SCCs more efficiently than Tarjan algorithm of linear complexity. However, on the one hand, as the theoretical basis of RST applied to SCCs discovery of digraphs, the theoretical relationships between RST and graph theory investigated in previous work only include four equivalences between fundamental RST and graph concepts relating to SCCs. The reasonability of using the two RST operators to find SCCs still need to be investigated. On the other hand, it is found that there are three SCCs correlations between vertices after we use three RST concepts, R-related set, lower and upper approximation sets, to analyze SCCs. RSCC algorithm ignores these SCCs correlations so that the efficiency of RSCC is affected negatively. For the above two issues, firstly, we explore the equivalence between the two RST operators and Breadth-First Search (BFS) which is one of the most basic graph search algorithms and the most direct way to find SCCs. These equivalences explain the reasonability of using the two RST operators to find SCCs, and enrich the content of the theoretical relationships between RST and graph theory. Secondly, we design a granulation strategy according to these three SCCs correlations. Then an algorithm called GRSCC for finding SCCs of simple digraphs based on granulation strategy is proposed. Experimental results show that GRSCC provides better performance to RSCC.

An overlapping community detection algorithm based on rough clustering of links

The growth of networks is prevalent in almost every field due to the digital transformation of consumers, business and society at large. The unfolding of community structure in such real-world complex networks is crucial since it aids in gaining strategic insights leading to informed decisions. Moreover, the co-occurrence of disjoint, overlapping and nested community patterns in such networks demands methodologically rigorous community detection algorithms so as to foster cumulative tradition in data and knowledge engineering. In this paper, we introduce an algorithm for overlapping community detection based on granular information of links and concepts of rough set theory. First, neighborhood links around each pair of nodes are utilized to form initial link subsets. Subsequently, constrained linkage upper approximation of the link subsets is computed iteratively until convergence. The upper approximation subsets obtained during each iteration are constrained and merged using the notion of mutual link reciprocity. The experimental results on ten real-world networks and comparative evaluation with state-of-the-art community detection algorithms demonstrate the effectiveness of the proposed algorithm.

R-Ensembler: A greedy rough set based ensemble attribute selection algorithm with kNN imputation for classification of medical data

Background and ObjectiveRetrieving meaningful information from high dimensional dataset is an important and challenging task. Normally, medical dataset suffers from several issues such as curse of dimensionality problem, uncertainty, presence of missing values, non-relevant and redundant attributes, etc. Any machine learning technique applied on such data (without any preprocessing) by and large takes a considerable amount of computational time and may degrade the performance of the model. MethodsIn this article, R-Ensembler, a parameter free greedy ensemble attribute selection method is proposed adopting the concept of rough set theory by using the attribute-class, attribute-significance and attribute-attribute relevance measures to select a subset of attributes which are most relevant, significant and non-redundant from a pool of different attribute subsets in order to predict the presence or absence of different diseases in medical dataset. The main role of the proposed ensembler is to combine multiple subsets of attributes produced by different rough set filters and to produce an optimal subset of attributes for subsequent classification task. A novel n number of set intersection method is also proposed to reduce the biasness during the time of attribute selection process. Before selecting the minimal attribute set from a given data by the proposed R-Ensembler method, the dataset is preprocessed by the k nearest neighbour (kNN) imputation method for missing value treatment. ResultsExperiments are carried out on seven benchmark medical datasets collected from University of California at Irvine (UCI) repository. The performance of the proposed ensemble method is compared with five state-of-the-art attribute selection algorithms, results of which are measured using three benchmark classifiers viz., Naïve Bayes, decision trees and random forest. Experimental results clearly justify the superiority of the proposed R-Ensembler method over other attribute selection algorithms. Results of paired t-test performed on average accuracies produced by different classifiers simulated on the reduced data sets achieved by the proposed and counter part attribute selection methods confirm the statistical significance of the better reduced attribute subsets achieved by the proposed R-Ensembler method compared to others. ConclusionThe proposed ensemble method turned out to be very effective for selecting high relevant, high significant and less redundant attributes from a pool of different subsets of attributes.

A topological method for reduction in digital information uncertainty

An attribute reduct, an important concept of rough set theory, is a subset that is sufficient and individually necessary for preserving a particular property of the given information system. In this study, we present a proposed method to calculate the accuracy of data by using the concepts of pre-open and semi-open. We also compared the results of accuracies in the proposed method with the accuracies in Yao and Pawlak methods. Our study revealed that the new model calculating the degree of accuracy was better than the previous models. Additionally, we provided a new insight into the application of the attribute reduction and we used MATLAB programming to obtain the result.

An IDS Alerts Aggregation Algorithm Based on Rough Set Theory

Within a system in which has been deployed several IDS, a great number of alerts can be triggered by a single security event, making real alerts harder to be found. To deal with redundant alerts, we propose a scheme based on rough set theory. In combination with basic concepts in rough set theory, the importance of attributes in alerts was calculated firstly. With the result of attributes importance, we could compute the similarity of two alerts, which will be compared with a pre-defined threshold to determine whether these two alerts can be aggregated or not. Also, time interval should be taken into consideration. Allowed time interval for different types of alerts is computed individually, since different types of alerts may have different time gap between two alerts. In the end of this paper, we apply proposed scheme on DAPRA98 dataset and the results of experiment show that our scheme can efficiently reduce the redundancy of alerts so that administrators of security system could avoid wasting time on useless alerts.

A group incremental feature selection for classification using rough set theory based genetic algorithm

Data Mining is one of the most challenging tasks in a dynamic environment due to rapid growth of data with respect to time. Dimension reduction, the key process of relevant feature selection, is applied prior to extracting interesting patterns or information from large repositories of data. In a dynamic environment, newly generated group of data together with the information extracted from the previous data are analyzed to select the most relevant and important features of the entire data set. As a result, efficiency and acceptability of the incremental feature selection model increase in the field of data mining. In our paper, a group incremental feature selection algorithm is proposed using rough set theory based genetic algorithm for selecting the optimized and relevant feature subset, called reduct. The objective function of the genetic algorithm used for incremental feature selection is defined using the previously generated reduct and positive region of the target set, concepts of rough set theory. The method may be applied in a regular basis in the dynamic environment after small to moderate volume of data being added into the system and thus the computational time, the major issue of the genetic algorithm does not affect the proposed method. Experimental results on benchmark datasets demonstrate that the proposed method provides satisfactory results in terms of number of selected features, computation time and classification accuracies of various classifiers.

Attribute selection for improving spam classification in online social networks: a rough set theory-based approach

As online social network (OSN) sites become increasingly popular, they are targeted by spammers who post malicious content on the sites. Hence, it is important to filter out spam accounts and spam posts from OSNs. There exist several prior works on spam classification on OSNs, which utilize various features to distinguish between spam and legitimate entities. The objective of this study is to improve such spam classification, by developing an attribute selection methodology that helps to find a smaller subset of the attributes which leads to better classification. Specifically, we apply the concepts of rough set theory to develop the attribute selection algorithm. We perform experiments over five different spam classification datasets over diverse OSNs and compare the performance of the proposed methodology with that of several baseline methodologies for attribute selection. We find that, for most of the datasets, the proposed methodology selects an attribute subset that is smaller than what is selected by the baseline methodologies, yet achieves better classification performance compared to the other methods.