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Ever since the introduction of rough sets by Pawlak as a model to capture uncertainty, it has drawn much attention from both theoretical and application point of view. Classifications of universes play very important roles in several fields of study. The study of rough definability of classifications was initiated by Busse. The properties of approximations of classifications were established in the form of four theorems and were used to define the types of classifications. These results were generalised to develop two theorems of necessary and sufficient type were established by Tripathy et al , from which several results including the four theorems of Busse could be derived as corollaries. Recently, rough sets based on Multigranulation were introduced and studied by Qian et al. Also, it has been extended to include incomplete information systems. Many of these results are extended to the multigranular cases. In this paper, we extend the properties of types of classifications to the multigranular context. Also, we introduce some parameters like the accuracy of approximation and the quality of approximation of classifications with respect to Multigranulations. We have obtained interesting criteria under which both types of Multigranulations reduce to single granulation. Also, some algebraic properties of Multigranulations are derived

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With the advancements in the WWW and ICT, the e-learning domain has developed very fast. Even many educational institutions these days have shifted their focus towards the e-learning and mobile learning environments. However, from the quality of learning point of view, which is measured in terms of "active learning" taking place, the e-learning environment lags behind the traditional classroom based learning. One of the reasons for that is the availability of large volumes of static and unorganized contents over the e-learning environment which makes it difficult for learners to precisely identify the contents matching with their requirements. With the modern day e-learning environments providing the digital contents to their learners in the form of Learning Objects (LOs), creation of such LOs by proper composition along with meaningful metadata will help the learners to retrieve them precisely. The focus of this work is to address the issues related to imparting active learning over an e-learning environment through LOs. This paper proposes a new method to compose, share, reuse, and manage objects based on the principles of the Object Oriented Paradigm (OOP). The Learning Object Composition and Presentation System (LOCPS) developed as a part of this work has shown better results in precisely retrieving the objects matching with the learner requirements.

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Abstract-Detection of affected areas in images is a crucial step in assessing the depth of the affected area for municipal operators. These affected areas in the underground images, which are line images are indicative of the condition of buried infrastructures like sewers and water mains. These images identify affected areas and extract their properties like structures from the images, whose contrast has been enhanced.. . A Centroid Model for the Depth Assessment of Images using Rough Fuzzy Set Techniques presents a three step method which is a simple, robust and efficient one to detect affected areas in the underground concrete images. The proposed methodology is to use segmentation and feature extraction using structural elements. The main objective for using this model is to find the dimensions of the affected areas such as the length, width, depth and the type of the defects/affected areas. Although human eye is extremely effective at recognition and classification, it is not suitable for assessing defects in images, which might have spread over thousands of miles of image lines. The reasons are mainly fatigue, subjectivity and cost. Our objective is to reduce the effort and the labour of a person in detecting the affected areas in underground images. A proposal to apply rough fuzzy set theory to compute the lower and upper approximations of the affected area of the image is made in this paper. In this connection we propose to use some concepts and technology developed by Pal and Maji.

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A major challenge in biomedical studies in recent years has been the classification of gene expression profiles into categories, such as cases and controls. This is done by first training a classifier by using a labeled training set containing labeled samples from the two populations, and then using that classifier to predict the labels of new samples. Such predictions have recently been shown to improve the diagnosis and treatment selection practices for several diseases. This procedure is complicated, however, by the high dimensionality of the data. While microarrays can measure the levels of thousands of genes per sample, case-control microarray studies usually involve no more than several dozen samples. Standard classifiers do not work well in these situations where the number of features (gene expression levels measured in these microarrays) far exceeds the number of samples. Selecting only the features that are most relevant for discriminating between the two categories can help construct better classifiers, in terms of both accuracy and efficiency. This paper provides a comparison between dimension reduction technique, namely Partial Least Squares (PLS)method and a hybrid feature selection scheme, and evaluates the relative performance of four different supervised classification procedures such as Radial Basis Function Network (RBFN), Multilayer Perceptron Network (MLP), Support Vector Machine using Polynomial kernel function(Polynomial-SVM) and Support Vector Machine using RBF kernel function (RBF-SVM) incorporating those methods. Experimental results show that the Partial Least-Squares(PLS) regression method is an appropriate feature selection method and a combined use of different classification and feature selection approaches makes it possible to construct high performance classification models for microarray data.