Fuzzy rough set theory

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OWA-FRPS : a prototype selection method based on ordered weighted average fuzzy rough set theory

OWA-FRPS : a prototype selection method based on ordered weighted average fuzzy rough set theory

Although many researchers have focused on developing fuzzy rough feature se- lection [11] algorithms, there is not much literature on fuzzy rough PS yet. Nevertheless, fuzzy rough set theory [12] is a good tool to model noisy data. To the best of our knowledge, the only fuzzy rough based PS method is FRIS [13]. This method selects those instances that have a fuzzy positive region higher than a certain threshold. This method has some problems, the main one being that the method’s performance highly relies on a good threshold selection. In this work, we propose a new fuzzy rough based PS method that assesses the quality of instances using Ordered Weighted Average (OWA) fuzzy rough set theory [14], a more robust version of fuzzy rough set theory, and automatically selects an appropriate threshold.
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Diagnosis of Cancer using Fuzzy Rough Set Theory

Diagnosis of Cancer using Fuzzy Rough Set Theory

A hybrid intelligent classification model for medical data consists of Fuzzy Min–Max Neural Network [11], Regression tree and the Random Forest algorithm [11]. Regression tree [11] is operated by building a number of decision trees at training timebut their algorithm is slow for real time prediction due to large number of trees. A series of empirical studies using three benchmark medical datasets from the UCI Machine Learning Repository, namely Breast Cancer Wisconsin, Liver Disorders, and Pima Indians Diabetes has been used to evaluate the efficiency of the hybrid model. Different experimental configurations have been adopted in order to provide a fair performance comparison with different models reported in the literature. The main contribution of this paper is the hybrid model that possesses three important characteristics for tackling medical decision support tasks such as online learning, high performance, and rule extraction.
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A Distributed Clustering Approach for Heterogeneous Environments  Using Fuzzy Rough Set Theory

A Distributed Clustering Approach for Heterogeneous Environments Using Fuzzy Rough Set Theory

The second type of instances that our algorithm avoids sending them to the central location is boundary instances. Boundary instances are in the boundary of clusters where the clustering algorithm has the low uncertainty about true cluster that instances should belong to. We omit the label of boundary instances to central location. In order to show how FRIW is able to select boundary instances, we examine FRIW on 8d5k data set. 8d5k has eight dimensions and five clusters. We project instances on two principal dimensions. The left side of Figure 3 illustrates the scatter view of instances in two dimensions. The right side of this figure shows the scatter view of instances after selecting boundary instances with FRIW. It is apparent that FRIW can find the boundary instances according to their weights. This promising experiment shows that FRIW can be used as standalone boundary detection algorithm for other purposes in future.
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HRNeuro-fuzzy: Adapting neuro-fuzzy classifier for recurring concept drift of evolving data streams using rough set theory and holoentropy

HRNeuro-fuzzy: Adapting neuro-fuzzy classifier for recurring concept drift of evolving data streams using rough set theory and holoentropy

streams based on the class labels of previous data stream. Ini- tially, the input database was given to the Principal Compo- nent Analysis for dimension reduction. Then, the database was divided into data chunks which were employed to build the neuro fuzzy system by the bell shaped membership func- tion. The concept change was detected using the accuracy of approximation which was compared with the threshold value. Thus, the rough set theory was used in this paper to estimate the accuracy of approximation of the data set. Then, the updating behaviour of neuro fuzzy system was required to update the membership function and fuzzy rules. Finally, the data stream was classified based on the previous data stream after updating the fuzzy system. The experimental results of the proposed system were evaluated for the breast cancer data- set, localization dataset and skin segmentation dataset. Then, the performance of these datasets were analysed using the met- rics such as precision, recall, F-measure, computation time and accuracy. The higher accuracy of 96% was acquired by the proposed neuro fuzzy system for the better classification of data stream.
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Covering-Based Grade Rough Fuzzy Set Models

Covering-Based Grade Rough Fuzzy Set Models

membership in the minimum description. At the same time, we note that the fuzzy set theory and the rough set model have strong complementarity to each other as mathematical tools to describing and handling uncertain knowledge. Rough set theory is mainly used for knowledge discovery and decision-making in uncertain or incomplete information systems, the basis theorem of the Rough set theory is to approximate the research objects by using the determined upper and lower approximation. Particularly, this descriptive process doesn’t need to preprocess the data or providing any priori knowledge. Different from the rough set theory, the fuzzy set theory is mainly used to describe and handle the problem of fuzzy information or concept. In addition, it often needs to rely on the prior knowledge, such as expert systems. As a generalization of the classical rough set theory, Dabois et al. proposed the concept of fuzzy rough sets and rough fuzzy sets in 1990, and their properties have been researched at the same time [20,21,22]. Based on the discussion of the covering rough set models and the overlapping information between the set and the equivalence classed proposed in this paper, four kinds of covering grade rough fuzzy set models are defined and established by means of the minimum description of neighbor domain, whole neighborhood, rule confidence and membership of the elements. It unifies the results of predecessors. In addition, their properties and relationships are discussed. Finally, an example is given.
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Predictive modeling for telco customer 
		churn using rough set theory

Predictive modeling for telco customer churn using rough set theory

Rough set has been used worldwide in numerous applications, including feature selection [11], stock market prediction [12] and hybridisation with fuzzy set. Rough set has already been used for medical image segmentation [13] and designing diabetic diagnose system in India [14]. Rough set also has a good research base in multimedia data management [15] and accident chain exploration [16]. The approximation concept in Rough Set can be implemented for classifying customer churn. In short, employing rough set to classify customer churn is currently relevant.
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The Application of Fuzzy-Rough Set Decision Tree for Credit Rating

The Application of Fuzzy-Rough Set Decision Tree for Credit Rating

Decision tree technique has been shown to independently interpret problems and can solve the problem on a large scale , but this technique is also known as the classification technique with a high level of instability with respect to interference in training data and way of presenting the data with a high variance . Fuzzy theory can increase endurance when performing classification of new cases in a decision tree . Fuzzy logic led to improvements in this aspect because the elasticity of fuzzy sets . The method aim shave been studied in detail and crisp been compared with alternative method and the results showed much improvement from accuray level of prediction results , shown with much reduced variance models . In addition, fuzzy logic is also more stable at a level better than parameters interpreted . Fuzzy decision tree based on fuzzy rough techniques is a new criterion based on a meeting between fuzzy conditional attributes with attribute fuzzy decision to select attributes that will be expanded . Fuzzy conditional attributes will be selected as the most important attribute to be expanded . For a given FIS , every fuzzy conditional attribute has a different contribution to the fuzzy decision attribute , relationship
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A fuzzy neighborhood rough set method for anomaly detection in large scale data

A fuzzy neighborhood rough set method for anomaly detection in large scale data

Rough set theory RST [10-11] is a new mathematical approach to imperfect knowledge. The theory has attracted attention of many researchers and practitioners all over the world, who contributed essentially to its development and applications. The main advantage of rough set theory in data analysis is that it does not need any preliminary or additional information about data. Rough set theory is a popular and powerful machine learning tool. It is especially suitable for dealing with information systems that exhibit inconsistencies. In rough set theory, an information table is defined as a tuple T = (U, A) where U and A are two finite, non-empty sets with U the universe of primitive objects and A the set of attributes. Each attribute or feature a ∈ A is associated with a set V a of its value, called the domain of a. We may partition the attribute set A into two subsets C and
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An Innovative Approach for Attribute Reduction in Rough Set Theory

An Innovative Approach for Attribute Reduction in Rough Set Theory

Real world informations are often uncertain, vague or incomplete due to difficulties associated to record or re- port any natural phenomena or events that are under study. Some approaches are well known to tackle such is- sues, mainly the Fuzzy Set theory [9], the Dempster-Shafer theory [10] [11], and the possibility theory [12]. In the beginning of the eighties, another theory emerged for treating such kind of information, the Rough Set Theory-RST [1]. This theory is simple and has a good mathematical formalism. It is an extension of the set theory that deals with data uncertainty by means of an equivalence relation known as indiscernibility. Two ele- ments of a given set are considered as indiscernible if they present the same properties, according to a defined set of features, attributes or variables. Some authors like [13] point out that the main advantage of RST is not requiring additional informations such as the probability distribution, a priori probability or pertinence degree.
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A Study on Rough, Fuzzy and Rough Fuzzy Bi-ideals of Ternary Semigroups

A Study on Rough, Fuzzy and Rough Fuzzy Bi-ideals of Ternary Semigroups

The notion of fuzzy sets was introduced by Zadeh [23]. Fuzzy set theory is a generalization of set theory. Applica- tions of the fuzzy set theory have been found in various fields. The notion of rough sets was introduced by Pawlak [16]. Rough set is described by a pair of ordinary sets called the upper and lower approximations. The notion of a rough set has often been compared to that of a fuzzy set, sometimes with a view to prove that one is more general, or, more useful than the other. Several researchs were conducted on the generalizations of the notion of fuzzy sets and rough sets. The fuzzy sets and rough sets were studied in various kinds of algebraic systems. Moreover, they were studied in various kinds of ternary algebraic systems. For example, Kavikumar and Khamis [10] studied fuzzy ideals and fuzzy quasi- ideals in ternary semirings, Kavikumar, Khamis and Jun [11] studied fuzzy bi-ideals in ternary semirings, Chinram and Malee studied L-fuzzy ideals [1] and k-fuzzy ideals [15] in ternary semirings, Davvaz [3] studied fuzzy hyperideals in ternary semihyperrings and Chinram and Saelee [2] studied fuzzy ideals and fuzzy filters of ordered ternary semigroups, etc. Rough ideals in semigroups were studied by Kuroki [12]. In [22], Xiao and Zhang studied rough prime ideals and rough fuzzy prime ideals. Later, Petchkhaew and Chinram [17] studied rough ideals and fuzzy rough ideals of ternary semigroups analogous to that of semigroups considered by
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Autonomous clustering using rough set theory

Autonomous clustering using rough set theory

Cluster analysis is an important exploratory technique for discovering patterns and underlying structure in data. The aim of clustering is to partition a data set into classes such that within-class homogeneity is high and between-class homogeneity weak. However, standard clustering techniques, including agglomerative hierarchical algorithms, K-means clustering and fuzzy c-means clustering, carry a number of inherent problems that directly influence the clustering solution. In all cases, a high degree of subjectivity is required to obtain an ‘optimal’ clustering solution. This results in a non- unified approach to clustering, allowing for different clusters to be obtained when a given technique is applied to the same data by different people. This puts the optimality of any given solution under scrutiny in terms of how well it really reflects true underlying data structures. Furthermore, the standard techniques generally focus on the clustering of single-type attribute data sets (e.g. continuous attributes) and are unable to cope easily with mixed attribute data. In terms of clustering applications, such as medical data, this is a major disadvantage.
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Image Segmentation using Rough Set based Fuzzy K means Algorithm

Image Segmentation using Rough Set based Fuzzy K means Algorithm

Rough Set Theory was firstly introduced by Pawlak in 1982 [2][3],and is a valuable mathematical tool for dealing with vagueness and uncertainty [4]. Similar or indiscernibility relation is the mathematical basis of the Rough Set theory. The key concept of rough set theory is the approximate equality of sets in a given approximation space [2][3]. An approximation space A is an ordered pair ( , ) U R , where U is a certain set called universe, and that equivalence relation R   U U is a binary relation called indiscernibility relation; if x y ,  U any ( , ) x y  R , this means that x and y are indistinguishable in A ; equivalence classes of the relation R are called elementary sets (atoms) in A (an empty set is also elementary), and the set of all atoms in A is denoted by U R / . In the Rough Set approach, any vague concept is characterized by a pair of precise concepts, that is the lower and upper approximation of the vague concept. Let X  U be a subset of U , then the lower and upper approximation of X in A are respectively denoted as:
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Fuzzy-Rough Set Bireducts for Data Reduction

Fuzzy-Rough Set Bireducts for Data Reduction

The increase in the popularity of rough sets is largely the result of a series of desirable theoretical aspects. Indeed, the grouping of information into equivalence classes is intuitive and offers a certain universal appeal. Additionally, RST possesses other properties that are advantageous. Parameters are not needed, thus obviating any requirement for user input, which is subjective and potentially erroneous. RST also determines a representation of the data that is minimal. However, the primary obstacle for traditional rough set theory is that it can only be applied to crisp or discrete-valued data. This inability to handle real-valued and noisy data has led to the exploration of approaches which hybridise RST with other techniques. One of these hybridisations is fuzzy-rough sets [3] which offer the ability to model fuzzy uncertainty in both the conditional and decision attributes.
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A New Approach to Rough Lattices and Rough Fuzzy Lattices Based on Fuzzy Ideals

A New Approach to Rough Lattices and Rough Fuzzy Lattices Based on Fuzzy Ideals

I T is well known that, in the real world, classical methods are not always successful in dealing with the problems in economy, engineering and social science, because of various types of uncertainties presented in these problems. As far as known, there are several theories to describe uncertainty, for example, fuzzy set theory [24], rough set theory [10] and other mathematical tools. Over these years, a lot of experts and scholars are looking for some different ways to solve the problem of uncertainty.

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A Variable Precision Fuzzy Rough Set Approach to a Fuzzy Rough Decision Table

A Variable Precision Fuzzy Rough Set Approach to a Fuzzy Rough Decision Table

The rough set theory and fuzzy set theory are extensions of classical set theory, and they are related but distinct and complementary theories. The rough set theory[1,2] is mainly focused on crisp information granulation, while its basic concept is indiscernibility, for example, an indiscernibility between different objects deduced by different attribute values of described objects in the information system; whereas the fuzzy set theory is regarded as a mathematical tool for imitating the fuzziness in the human classification mechanism, which mainly deals with fuzzy information granulation. Because of its simplicity and similarity with the human mind, its concept is always used to express quantity data expressed by language and membership functions in the intelligent system. In fuzzy sets, the attributes of elements may be between yes and no. For example, a beautiful scenery, we cannot simply classify the beautiful scenery into a category between yes and no. For the set of beautiful scenery, there does not exist good and definite border. The fuzzy sets cannot be described with any precise mathematical formula, but it is included in the physical and psychological process of human's way of thinking, because the physiology of human reasoning is never used any precise mathematical formula during the physical process of reasoning, and fuzzy sets is important in the pattern classification. Essentially, these two theories both study the problems of information granularity. The rough set theory[3,4] studies rough non-overlapping type and the rough concept; while the fuzzy set theory studies the fuzziness between overlapping sets, and these naturally lead to investigating the possibility of the "hybrid" between the rough sets and the fuzzy set. The hybrid of rough set and fuzzy set can be divided into three kinds of approximations that are the approximations of fuzzy sets in a crisp space, the approximations of crisp sets in fuzzy approximate space, and the approximations of fuzzy sets in fuzzy approximate space[8,9]. The paper mainly discusses the second case. In order to simulate the situation of this type, Dubios introduced the concept of fuzzy rough sets (Dubois and Prade, 1990)[6], which is an extension of rough set approximation deduced from a crisp set in fuzzy approximate space.
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A Fast Host-Based Intrusion Detection System Using Rough Set Theory

A Fast Host-Based Intrusion Detection System Using Rough Set Theory

Abstract. Intrusion Detection system has become the main research focus in the area of information security. Last few years have witnessed a large variety of technique and model to provide increasingly efficient intrusion detection solutions. We advocate here that the intrusive behav- ior of a process is highly localized characteristics of the process. There are certain smaller episodes in a process that make the process intrusive in an otherwise normal stream. As a result it is unnecessary and most often misleading to consider the whole process in totality and to attempt to characterize its abnormal features. In the present work we establish that subsequences of reasonably small length of sequence of system calls would suffice to identify abnormality in a process. We make use of rough set theory to demonstrate this concept. Rough set theory also facilitates identifying rules for intrusion detection. The main contributions of the paper are the following- (a) It is established that very small subsequence of system call is sufficient to identify intrusive behavior with high ac- curacy. We demonstrate our result using DARPA’98 BSM data; (b) A rough set based system is developed that can extract rules for intrusion detection; (c) An algorithm is presented that can determine the status of a process as either normal or abnormal on-line.
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DYNAMIC REDUCTS IN OBJECT ORIENTED INFORMATION SYSTEM USING ROUGH SET THEORY

DYNAMIC REDUCTS IN OBJECT ORIENTED INFORMATION SYSTEM USING ROUGH SET THEORY

Rough set theory [1, 2] provides a theoretical foundation of approximation of objects. Information systems represent characteristics of objects by attributes and its values, and for any given concepts, that is, any subsets of objects, lower and upper approximations by indiscernibility relations illustrate set-theoretic approximations of concepts. However, “traditional” rough set theory has the following two constraints:

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E Learning Attributes Selection Through Rough Set Theory and Data Mining

E Learning Attributes Selection Through Rough Set Theory and Data Mining

Our work deals broadly with search methods for attribute selection which reduces the dimensionality of the search space. This approach has got three steps. Firstly is to identify the attributes to be selected, secondly is to check the selected attributes for the possibility of higher performance and finally to terminate the searching with threshold conditions. The same approach is tested with two independent tools one based on rough set theory called ‘ROSE’ (ROugh Set Explorer) and another based on machine learning algorithms called ‘Weka’ (Waikato environment for Knowledge Analysis). We mainly apply supervised algorithms for classification in more than one iteration in order to identify the useful attributes. The attributes are representing the significant events in the engagement of students and hence the accuracy of predictions are enhanced by
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Rough Set based Natural Image Segmentation under Game Theory Framework

Rough Set based Natural Image Segmentation under Game Theory Framework

Abstract- The Since past few decades, image segmentation has been successfully applied to number of applications. When different image segmentation techniques are applied to an image, they produce different results especially if images are obtained under different conditions and have different attributes. Each technique works on a specific concept, such that it is important to decide as to which image segmentation technique should for a given application domain. On combining the strengths of individual segmentation techniques, the resulting integrated method yields better results thus enhancing the synergy of the individual methods alone. This work improves the segmentation technique of combining results of different methods using the concept of game theory. This is achieved through Nash equilibrium along with various similarity distance measures. Using game theory the problem is divided into modules which are considered as players. The number of modules depends on number of techniques to be integrated. The modules work in parallel and interactive manner. The effectiveness of the technique will be demonstrated by simulation results on different sets of test images.
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CHANGING TRENDS OF PREFERENCES IN MODE OF TRANSACTIONS A PREDICTION USING ROUGH SET THEORY

CHANGING TRENDS OF PREFERENCES IN MODE OF TRANSACTIONS A PREDICTION USING ROUGH SET THEORY

Rough Set Theory is a new technique that deals with fuzziness and improbability stressed in decision making. Data mining is a discipline that has an important contribution to data analysis, discovery of new significant knowledge, and independent decision making. The rough set theory offers a feasible approach for decision rule extraction from data. The introduction of demonetisation resulted in elimination of high valued currency notes. It aimed to achieve the goal of a ‘less cash’ society. Digital trades bring in better scalability and responsibility. Recently RBI has also disclosed its document- “Payments and Settlement Systems in India: Vision 2018” boosting the electronic payments and to help INDIA grow from cash to cashless society in the long run. Thus giving this model an overlook, this paper focuses on studying the views of people on evolution of cashless economy and their comfort level with it. The study was conducted in Chennai; data was collected with the help of organised questionnaire and analysed using rough set theory.
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