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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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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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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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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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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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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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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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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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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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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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.

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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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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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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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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