Rough Sets were introduced by Z. Pawlak in the year 1982 with the intention to address knowledge representation and data processing from the angle of computation and decision making. The main idea...

Information is considered to be the major part of an organization. With the enhancement of technology, the knowledge level is increasing with the passage of time. This increase of information is in volume, velocity, and variety. Extracting meaningful insights is the dire need of an individual from such information and knowledge. Visualization is a key tool and has become one of the most significant platforms for interpreting, extracting, and communicating information. The current study is an endeavour toward data modelling and (...) user knowledge by using a rough set approach for extracting meaningful insights. The technique has used different rough set algorithms such as K-nearest neighbours, decision rules, decomposition tree, and local transfer function classifier for an experimental setup. The approach has found its accuracy for the optimal use of data modelling and user knowledge. The experimental setup of the proposed method is validated by using the dataset available in the UCI web repository. Results of the proposed study show that the model is effective and efficient with an accuracy of 96% for KNN, 87% for decision rules, 91% for decision trees, 85.04% for cross validation architecture, and 94.3% for local transfer function classifier. The validity of the proposed classification algorithms is tested using different performance metrics such as F-score, precision, accuracy, recall, specificity, and misclassification rates. For all these performance metrics, the KNN classifier outperformed, and this high performance shows the applicability of the KNN classifier in the proposed problem. (shrink)

The basic methodology of rough set theory depends on an equivalence relation induced from the generated partition by the classification of objects. However, the requirements of the equivalence relation restrict the field of applications of this philosophy. To begin, we describe two kinds of closure operators that are based on right and left adhesion neighbourhoods by any binary relation. Furthermore, we illustrate that the suggested techniques are an extension of previous methods that are already available in the literature. As (...) a result of these topological techniques, we propose extended rough sets as an extension of Pawlak’s models. We offer a novel topological strategy for making a topological reduction of an information system for COVID-19 based on these techniques. We provide this medical application to highlight the importance of the offered methodologies in the decision-making process to discover the important component for coronavirus infection. Furthermore, the findings obtained are congruent with those of the World Health Organization. Finally, we create an algorithm to implement the recommended ways in decision-making. (shrink)

Rough sets are used in numerous knowledge representation contexts and are then empowered with varied ontologies. These may be intrinsically associated with ideas of rationality under certain conditions. In recent papers, specific granular generalisations of graded and variable precision rough sets are investigated by the present author from the perspective of rationality of approximations (and the associated semantics of rationality in approximate reasoning). The studies are extended to ideal-based approximations (sometimes referred to as subsethood-based approximations). It (...) is additionally shown that co-granular or point-wise approximations defined by σ-ideals/filters (for an arbitrary relation σ) fit easily into the entire scheme. Concepts of the rationality of objects (vague or crisp) and their types are introduced and are shown to be applicable to most general rough sets by the present author. Surprising results on these are proved on these by her in this part of the research paper. The present paper is the first of a three part study on the topic. (shrink)

The standard Pawlak approach to rough set theory, as an approximation space consisting of a universe U and an equivalence (indiscernibility) relation R U x U, can be equivalently described by the induced preclusivity ("discernibility") relation U x U \ R, which is irreflexive and symmetric.We generalize the notion of approximation space as a pair consisting of a universe U and a discernibility or preclusivity (irreflexive and symmetric) relation, not necessarily induced from an equivalence relation. In this case the (...) "elementary" sets are not mutually disjoint, but all the theory of generalized rough sets can be developed in analogy with the standard Pawlak approach. On the power set of the universe, the algebraic structure of the quasi fuzzy-intuitionistic "classical" (BZ) lattice is introduced and the sets of all "closed" and of all "open" definable sets with the associated complete (in general nondistributive) ortholattice structures are singled out. (shrink)

In the paper we explore the idea of describing Pawlak’s rough sets using three-valued logic, whereby the value t corresponds to the positive region of a set, the value f — to the negative region, and the undefined value u — to the border of the set. Due to the properties of the above regions in rough set theory, the semantics of the logic is described using a non-deterministic matrix (Nmatrix). With the strong semantics, where only the (...) value t is treated as designated, the above logic is a “common denominator” for Kleene and Łukasiewicz 3-valued logics, which represent its two different “determinizations”. In turn, the weak semantics—where both t and u are treated as designated—represents such a “common denominator” for two major 3-valued paraconsistent logics. We give sound and complete, cut-free sequent calculi for both versions of the logic generated by the rough set Nmatrix. Then we derive from these calculi sequent calculi with the same properties for the various “determinizations” of those two versions of the logic (including Łukasiewicz 3-valued logic). Finally, we show how to embed the four above-mentioned determinizations in extensions of the basic rough set logics obtained by adding to those logics a special two-valued “definedness” or “crispness” operator. (shrink)

Labels provide a quick and effective solution to obtain people interesting content from large-scale social network information. The current interest label extraction method based on the subgraph stream proves the feasibility of the subgraph stream for user label extraction. However, it is extremely time-consuming for constructing subgraphs. As an effective mathematical method to deal with fuzzy and uncertain information, rough set-based representations for subgraph stream construction are capable of capturing the uncertainties of the social network. Therefore, we propose an (...) effective approach called RS_UNITE_SS, which is suitable for large-scale social network user interest label extraction. Specifically, we first propose the subgraph division algorithm to construct a subgraph stream by incorporating a rough set. Then, the algorithm for user real-time interest label extraction based on upper approximation is proposed by using sequentially characteristics of the subgraph. Empirically, we evaluate RS_UNITE_SS over real-world datasets, and experimental results demonstrate that our proposed approach is more computationally efficient than existing methods while achieving higher precision value and MRR value. (shrink)

This Paper combines interval- valued neutrouphic sets and rough sets. It studies roughness in interval- valued neutrosophic sets and some of its properties. Finally we propose a Hamming distance between lower and upper approximations of interval valued neutrosophic sets.

The present paper deals with the problem of evaluating empirical evidence for therapeutic decisions in medicine. The article discusses the views of Nancy Cartwright and John Worrall on the function that randomization plays in ascertaining causal relations with reference to the therapies applied. The main purpose of the paper is to present a general idea of alternative method of evaluating empirical evidence. The method builds on data analysis that makes use of rough set theory. The first attempts to apply (...) the method show that it is an interesting alternative to randomized controlled trials. (shrink)

In this paper, we defined (I,T) − standard neutrosophic rough sets based on an implicator I and a t-norm T on I; lower and upper approximations of standard neutrosophic sets in a standard neutrosophic approximation are defined. Some properties of (I,T) − standard neutrosophic rough sets are investigated. We consider the case when the neutrosophic components (truth, indeterminacy, and falsehood) are totally dependent, single-valued, and hence their sum is ≤ 1.

Rough set theory has been successfully applied to many fields, such as data mining, pattern recognition, and machine learning. Kernel rough sets and neighborhood rough sets are two important models that differ in terms of granulation. The kernel rough sets model, which has fuzziness, is susceptible to noise in the decision system. The neighborhood rough sets model can handle noisy data well but cannot describe the fuzziness of the samples. In this (...) study, we define a novel model called kernel neighborhood rough sets, which integrates the advantages of the neighborhood and kernel models. Moreover, the model is used in the problem of feature selection. The proposed method is tested on the UCI datasets. The results show that our model outperforms classic models. (shrink)

In this paper, we first defined soft intervalvalued neutrosophic rough sets(SIVN- rough sets for short) which combines interval valued neutrosophic soft set and rough sets and studied some of its basic properties. This concept is an extension of soft interval valued intuitionistic fuzzy rough sets( SIVIF- rough sets). Finally an illustartive example is given to verfy the developped algorithm and to demonstrate its practicality and effectiveness.

The work broadens – to a considerable extent – Z. Pawlak’s original method (1982, 1992) of approximation of sets. The approximation of sets included in a universum U goes on in the contextual approximation space CAS which consists of: 1) a sequence of Pawlak’s approximation spaces (U,Ci), where indexes i from set I are linearly ordered degrees of contexts (I, <), and Ci is the universum partition U, 2) a sequence of binary relations on sets included in (...) U, relations called context relations indexed with degrees of contexts. The introduction of relations of contexts of sets was inspired by the work of W. Ziarnko (1993). Intuitively, set X is the context of set Y to the degree i, when on the basis of knowledge of the elements of set X we can obtain knowledge about the belonging of these elements to set Y to the degree i which is a degree of uncertainty or ambiguity, or inaccuracy. The operations of approximation of sets Ci-, BNi, Ci+, called lower approximation of the degree i, boundary of the degree i, upper approximation of the degree i, are formulated in a way which is analogous with the systems of Pawlak’s approximation, by expanding their formulas accordingly. In the next part of the work, it is shown (in an analogous way to Bryniarski’s work (1989)) that one can define the following operations on contextual rough sets: the union of contextual rough sets, the intersection of contextual rough sets and the complement of contextual rough set. It is proved that the algebra of contextual rough sets is a ditributive lattice with a unit and with a zero. On the basis of the results presented above the problem of defining operations on contextual rough sets by membership relations (Bryniarski 1989) may be formulated analogously to the classical operations on sets. (shrink)

The rough set theory has interesting properties such as that a rough set is considered as distinct sets in distinct knowledge bases, and that distinct rough sets are considered as one same set in a certain knowledge base. This leads to a significant philosophical interpretation: a concept (or phenomenon) may be understood as different ones in different philosophical perspectives, while different concepts (or phenomena) may be understood as a same one in a certain philosophical perspective. (...) Such properties of rough set theory produce a mathematical model to support critical realism and the theory ladenness of observation in the philosophy of science. (shrink)

The existing fuzzy rough set models all believe that the decision attribute divides the sample set into several “clear” decision classes, and this data processing method makes the model sensitive to noise information when conducting feature selection. To solve this problem, this paper proposes a robust fuzzy rough set model based on representative samples. Firstly, the fuzzy membership degree of the samples is defined to reflect its fuzziness and uncertainty, and RS-FRS model is constructed to reduce the influence (...) of the noise samples. RS-FRS model does not need to set parameters for the model in advance and can effectively reduce the complexity of the model and human intervention. On this basis, the related properties of RS-FRS model are studied, and the sample pair selection algorithm based on RS-FRS is used for feature selection. In this paper, RS-FRS is tested and analysed on the open 12 datasets. The experimental results show that RS-FRS model proposed can effectively select the most relevant features and has certain robustness to the noise information. The proposed model has a good applicability for data processing and can effectively improve the performance of feature selection. (shrink)

We introduce an abstract framework for general rough set theory from a mereological perspective and consider possible concepts of ’a priori’ granules and granulation in the same. The framework is ideal for relaxing many of the relatively superfluous set-theoretic axioms and for improving the semantics of many relation based, cover-based and dialectical rough set theories. This is a relatively simplified presentation of a section in three different recent research papers by the present author.

Recently, big data analytics have gained significant attention in healthcare industry due to generation of massive quantities of data in various forms such as electronic health records, sensors, medical imaging, and pharmaceutical details. However, the data gathered from various sources are intrinsically uncertain owing to noise, incompleteness, and inconsistency. The analysis of such huge data necessitates advanced analytical techniques using machine learning and computational intelligence for effective decision making. To handle data uncertainty in healthcare sector, this article presents a novel (...) metaheuristic rough set-based feature selection with rule-based medical data classification technique on MapReduce framework. The proposed MRSFS-RMDC technique designs a butterfly optimization algorithm for minimal rough set selection. In addition, Hadoop MapReduce is applied to process massive quantity of data. Moreover, a rule-based classification approach named Repeated Incremental Pruning for Error Reduction is used with the inclusion of a set of conditional rules. The RIPPER will scale in a linear way with the number of training records utilized and is suitable to build models with data uncertainty. The proposed MRSFS-RMDC technique is validated using benchmark dataset and the results are inspected under varying aspects. The experimental results highlighted the supremacy of the MRSFS-RMDC technique over the recent state of art methods in terms of different performance measures. The proposed methodology has achieved a higher F-score of 96.49%. (shrink)

In this paper, we give an algebraic completeness theorem for constructive logic with strong negation in terms of finite rough set-based Nelson algebras determined by quasiorders. We show how for a quasiorder R, its rough set-based Nelson algebra can be obtained by applying Sendlewski’s well-known construction. We prove that if the set of all R-closed elements, which may be viewed as the set of completely defined objects, is cofinal, then the rough set-based Nelson algebra determined by the (...) quasiorder R forms an effective lattice, that is, an algebraic model of the logic E 0, which is characterised by a modal operator grasping the notion of “to be classically valid”. We present a necessary and sufficient condition under which a Nelson algebra is isomorphic to a rough set-based effective lattice determined by a quasiorder. (shrink)

Cancer is fast becoming an alarming cause of human death. However, it has been reported that if the disease is detected at an early stage, diagnosed, treated appropriately, the patient has better chances of survival long life. Machine learning technique with feature-selection contributes greatly to the detecting of cancer, because an efficient feature-selection method can remove redundant features. In this paper, a Fuzzy Preference-Based Rough Set (FPRS) blended with Support Vector Machine (SVM) has been applied in order to predict (...) cancer biomarkers for biological and gene expression datasets. Biomarkers are determined by deploying three models of FPRS, namely, Fuzzy Upward Consistency (FUC), Fuzzy Downward Consistency (FLC), and Fuzzy Global Consistency (FGC). The efficiency of the three models with SVM on five datasets is exhibited, and the biomarkers that have been identified from FUC models have been reported. (shrink)

Modern business judgment is mostly faced with complex, unclear nature, and not fully confirmed research objects and needs a lot of relevant data investigation, inherent contradiction retrieval, and the discovery and extraction of potential laws. Formulation of rules and evaluation of system uncertainty: Appropriate decisions can be made based on this. Rough set theory is a new mathematical tool to deal with uncertain knowledge. Therefore, the theory of rough set is helpful for decision-makers to solve the decision problems (...) of complex systems. The simplification of knowledge of information systems and incomplete information systems and the theoretical and methodological study of rule acquisition are the central issues of rough set theory and applied research. A variety of simplified theories and methods have been proposed from a variety of viewpoints. However, there are still many theoretical problems that need to be investigated and solved in these aspects. In addition, the investment environment is a complex organic system that includes economic environment, social environment, resource environment, infrastructure, and other factors. There are a variety of data to measure these factors, which are mutually restrictive and interdependent. At present, domestic and foreign scholars have basically formed a series of assessment methods and models of investment environment assessment, but most of these assessment methods are affected by the differences in the degree of subjective factors of evaluators and the establishment of index weights in the assessment process. In most cases, more reliance is placed on subjective, artificial assignments and scoring loops. Therefore, it is an appropriate and reasonable method to evaluate the investment environment through data to evaluate all the factors affecting the investment environment and reach a comprehensive evaluation conclusion, which can effectively avoid human subjective factors to a certain extent. (shrink)

“Rough set” is a theory put forward by the polish scholar Z. Pawlak, which is a useful mathematics tool for dealing with vague and uncertain information. Rough set theory can achieve a subset of all attribute which preserves the discernible ability of original features, by using the data only with no additional information. As a typical system of multi-agent, the decision-making system of soccer robot has the features of multi-layered, antagonism, and cooperation. On the bases of rough (...) set theory, this paper established a decision making system with complete information for soccer robot, and then reduce the condition and decision attributes and their values, to get the simply decision rules. On the otherwise, considering the situation of information loss, we study decision making of imperfect information system, extract the decision rules and calculate the reliability, so that the rules can assist the agent to make right decision in competition. The simulation result shows that the algorithm is correct and effective. (shrink)

Online social networks are highly dynamic and sparse. One of the main problems in analyzing these networks is the problem of predicting the existence of links between users on these networks: the link prediction problem. Many studies have been conducted to predict links using a variety of techniques like the decision tree and the logistic regression approaches. In this work, we will illustrate the use of the rough set theory in predicting links over the Facebook social network based on (...) homophilic features. Other supervised learning algorithms are also employed in our experiments and compared with the rough set classifier, such as naive Bayes, J48 decision tree, support vector machine, logistic regression, and multilayer perceptron neural network. Moreover, we studied the influence of the “common groups” and “common page likes” homophilic features on predicting friendship between users of Facebook, and also studied the effect of using the Jaccard coefficient in measuring the similarity between users’ homophilic attributes compared with using the overlap coefficient. We conducted our experiments on two different datasets obtained from the Facebook online social network, where users in each dataset live within the same geographical region. The results showed that the rough set classifier significantly outperformed the other classifiers in all experiments. The results also demonstrated that the common groups and the common page likes features have a significant influence on predicting the friendship between users of Facebook. Finally, the results revealed that using the overlap coefficient homophilic features provided better results than that of the Jaccard coefficient features. (shrink)

A structural theorem for Kleene algebras is proved, showing that an element of a Kleene algebra can be looked upon as an ordered pair of sets, and that negation with the Kleene property is describable by the set-theoretic complement. The propositional logic \ of Kleene algebras is shown to be sound and complete with respect to a 3-valued and a rough set semantics. It is also established that Kleene negation can be considered as a modal operator, due to (...) a perp semantics of \. Moreover, another representation of Kleene algebras is obtained in the class of complex algebras of compatibility frames. One concludes with the observation that \ can be imparted semantics from different perspectives. (shrink)

To realize the coordinated and sustainable development of hydropower projects and regional society, comprehensively evaluating hydropower projects’ influence is critical. Usually, hydropower project development has an impact on environmental geology and social and regional cultural development. Based on comprehensive consideration of complicated geological conditions, fragile ecological environment, resettlement of reservoir area, and other factors of future hydropower development in each country, we have constructed a comprehensive evaluation index system of hydropower projects, including 4 first-level indicators of social economy, environment, safety, (...) and fairness, which contain 26 second-level indicators. To solve the problem that existing models cannot evaluate dynamic nonlinear optimization, a projection pursuit model is constructed by using rough set reduction theory to simplify the index. Then, an accelerated genetic algorithm based on real number coding is used to solve the model and empirical study is carried out with the Y hydropower station as a sample. The evaluation results show that the evaluation index system and assessment model constructed in our paper effectively reduce the subjectivity of index weight. Applying our model to the social impact assessment of related international hydropower projects can not only comprehensively analyze the social impact of hydropower projects but also identify important social influencing factors and effectively analyze the social impact level of each dimension. Furthermore, SIA assessment can be conducive to project decision-making, avoiding social risks and social stability. (shrink)

Over the past 50 years, Nelson algebras have been extensively studied by distinguished scholars as the algebraic counterpart of Nelson's constructive logic with strong negation. Despite these studies, a comprehensive survey of the topic is currently lacking, and the theory of Nelson algebras remains largely unknown to most logicians. This paper aims to fill this gap by focussing on the essential developments in the field over the past two decades. Additionally, we explore generalisations of Nelson algebras, such as N4-lattices which (...) correspond to the paraconsistent version of Nelson's logic, as well as their applications to other areas of interest to logicians, such as duality and rough set theory. A general representation theorem states that each Nelson algebra is isomorphic to a subalgebra of a rough set-based Nelson algebra induced by a quasiorder. Furthermore, a formula is a theorem of Nelson logic if and only if it is valid in every finite Nelson algebra induced by a quasiorder. (shrink)

With the rapid development of Internet of Things technology, RFID technology has been widely used in various fields. In order to optimize the RFID system hardware deployment strategy and improve the deployment efficiency, the prediction of the RFID system identification rate has become a new challenge. In this paper, a neighborhood rough set and random forest combination model is proposed to predict the identification rate of an RFID system. Firstly, the initial influencing factors of the RFID system identification rate (...) are reduced using neighborhood rough set theory combined with the principle of heuristic attribute reduction of neighborhood weighted dependency, thus obtaining a kernel factor subset. Secondly, a random forest prediction model is established based on the kernel factor subset, and a confusion matrix is established using out-of-bag data to evaluate the prediction results. The test is conducted under the constructed RFID experimental environment, whose results showed that the model can predict the identification rate of the RFID system in a fast and efficient way, and the classification accuracy can reach 90.5%. It can effectively guide the hardware deployment and communication parameter protocol setting of the system and improve the system performance. Compared with BP neural network and other prediction models, NRS-RF has shorter prediction time and faster calculation speed. Finally, the validity of the proposed model was verified by the RFID intelligent archives management platform. (shrink)

Both neutrosophic sets theory and rough sets theory are emerging as powerful tool for managing uncertainty, indeterminate, incomplete and imprecise information .In this paper we develop an hybrid structure called “ rough neutrosophic sets” and studied their properties.

As a generalization of Zhan’s method, the present paper aims to define the family of complementary fuzzy β -neighborhoods and thus three kinds of covering-based multigranulation -fuzzy rough sets models are established. Their axiomatic properties are investigated. Also, six kinds of covering-based variable precision multigranulation -fuzzy rough sets are defined and some of their properties are studied. Furthermore, the relationships among our given types are discussed. Finally, a decision-making algorithm is presented based on the proposed operations (...) and illustrates with a numerical example to describe its performance. (shrink)

Security has become one of the important factors for any network communication and transmission of data packets. An organization with an optimal security system can lead to a successful business and can earn huge profit on the business they are doing. Different network devices are linked to route, compute, monitor, and communicate various real-time developments. The hackers are trying to attack the network and want to draw the organization’s significant information for its own profits. During the communication, if an intrusion (...) or eavesdropping occurs, it will lead to a severe disfigurement of the whole communication network, and the data will be controlled by wrong malicious users. Identification of attack is a way to identify the security violations and analyze the measures in a computer network. An identification system, which is effective and accurate, can add security to the existing system for secure and smooth communication among end to end nodes and can work efficiently in the identification of attack on data packets. The role of information security is to design and protect the entire data of networks and maintain its confidentiality, integrity, and availability for their right users. Therefore, there is a need for end to end security management, which will ensure the security and privacy of the network and will save the data inside networks from malicious users. As the network devices are growing, so the level of threats is also increasing for these devices. The proposed research is an endeavor toward the detection of data packets attack by using the rough set theory for a secure end to end communication. The experimental work was performed by the RSES tool. The accuracy of the K-NN was 88% for the total objects of 8459. For cross validation purposes, the decision rules and decomposition tree algorithms were used. The DR algorithm showed accuracy of 59.1%, while the DT showed accuracy of 61.5%. The experimental results of the proposed study show that the research is capable of detecting data packets attack. (shrink)

A rough fuzzy set is the result of the approximation of a fuzzy set with respect to a crisp approximation space. It is a mathematical tool for the knowledge discovery in the fuzzy information systems. In this paper, we introduce the concepts of rough standard neutrosophic sets and standard neutrosophic information system, and give some results of the knowledge discovery on standard neutrosophic information system based on rough standard neutrosophic sets.