Fuzzy Absolutes and Related Topics

The study on the fuzzy absolutes and related topics. The different kinds of extensions especially compactification formed a major area of study in topology. Perfect continuous mappings always preserve certain topological properties. The concept of Fuzzy sets introduced by the American Cyberneticist L. A Zadeh started a revolution in every branch of knowledge and in particular in every branch of mathematics. Fuzziness is a kind of uncertainty and uncertainty of a symbol lies in the lack of well-defined boundaries of the set of objects to which this symbol belongs. Introduce an s-continuous mapping from a topological space to a fuzzy topological space and prove that the image of an H-closed space under an s-continuous mapping is f-H closed. Here also proved that the arbitrary product fi and sum of  fi of the s-continuous maps fi are also s-continuous. The original motivation behind the study of absolutes was the problem of characterizing the projective objects in the category of compact spaces and continuous functions.

Some Generalizations of Fuzzy Metrizability

The main purpose of the study is to extent concept of the class of spaces called ‘generalized metric spaces’ to fuzzy context and investigates its properties. Any class of spaces defined by a property possessed by all metric spaces could technically be called as a class of ‘generalized metric spaces’. But the term is meant for classes, which are ‘close’ to metrizable spaces in some under certain kinds of mappings. The theory of generalized metric spaces is closely related to ‘metrization theory’. The class of spaces likes Morita’s M- spaces, Borges’s w-spaces, Arhangelskii’s p-spaces, Okuyama’s  spaces have major roles in the theory of generalized metric spaces. The thesis introduces fuzzy metrizable spaces, fuzzy submetrizable spaces and proves some characterizations of fuzzy submetrizable spaces, and also the fuzzy generalized metric spaces like fuzzy w-spaces, fuzzy Moore spaces, fuzzy M-spaces, fuzzy k-spaces, fuzzy -spaces study of their properties, prove some equivalent conditions for fuzzy p-spaces. The concept of a network is one of the most useful tools in the theory of generalized metric spaces. The -spaces is a class of generalized metric spaces having a network.

Investigations on the Dynamics of Combination Maps and the Analysis of Bifurcation in a Discontinuous Logistic Map

This thesis is a study of discrete nonlinear systems represented by one dimensional mappings.As one dimensional interative maps represent Poincarre sections of higher dimensional flows,they offer a convenient means to understand the dynamical evolution of many physical systems.It highlighting the basic ideas of deterministic chaos.Qualitative and quantitative measures for the detection and characterization of chaos in nonlinear systems are discussed.Some simple mathematical models exhibiting chaos are presented.The bifurcation scenario and the possible routes to chaos are explained.It present the results of the numerical computational of the Lyapunov exponents (λ) of one dimensional maps.This thesis focuses on the results obtained by our investigations on combinations maps,scaling behaviour of the Lyapunov characteristic exponents of one dimensional maps and the nature of bifurcations in a discontinous logistic map.It gives a review of the major routes to chaos in dissipative systems,namely, Period-doubling ,Intermittency and Crises.This study gives a theoretical understanding of the route to chaos in discontinous systems.A detailed analysis of the dynamics of a discontinous logistic map is carried out, both analytically and numerically ,to understand the route it follows to chaos.The present analysis deals only with the case of the discontinuity parameter applied to the right half of the interval of mapping.A detailed analysis for the n –furcations of various periodicities can be made and a more general theory for the map with discontinuities applied at different positions can be on a similar footing

Antimedian graphs

Antimedian graphs are introduced as the graphs in which for every triple of vertices there exists a unique vertex x that maximizes the sum of the distances from x to the vertices of the triple. The Cartesian product of graphs is antimedian if and only if its factors are antimedian. It is proved that multiplying a non-antimedian vertex in an antimedian graph yields a larger antimedian graph. Thin even belts are introduced and proved to be antimedian. A characterization of antimedian trees is given that leads to a linear recognition algorithm.

Organic Synthesis Mediated by Heterogeneous Catalysts

Catalysis is a technologically important field which determines the quality of life in future. Catalyst research in pharmaceutical industry,fine chemical synthesis and emission control demands supported catalysts in bulk quantities.In the present work it was observed that clay supported catalysts mentioned in various chapters could also be used for the synthesis of similar molecules. The K10Ti catalyst can be used for the synthesis similar substituted imidazole derivatives under solvent free conditions and synthetically important Mannich bases of substrates containing various substitutes.Al-pillared saponite can be used for acetalation of other polyhydroxy compounds like glycerol,mannitol etc.Cu-Pd KSF catalyst has found application in C-C bond forming reactions which can be applied to other reactions and similar methods can be adopted for the synthesis of other catalyst by changing the transition metals. Montmorillonite K10 catalysed synthesis of triarylpyridines can be extended to the synthesis tetrasubstuted pyroles.K10Ti can also be utilized for the synthesis of similar heterocycles.

Statistical Machine Learning Techniques for the Prediction of Learning Disabilities in School-Age Children

Learning Disability (LD) is a general term that describes specific kinds of learning problems. It is a neurological condition that affects a child's brain and impairs his ability to carry out one or many specific tasks. The learning disabled children are neither slow nor mentally retarded. This disorder can make it problematic for a child to learn as quickly or in the same way as some child who isn't affected by a learning disability. An affected child can have normal or above average intelligence. They may have difficulty paying attention, with reading or letter recognition, or with mathematics. It does not mean that children who have learning disabilities are less intelligent. In fact, many children who have learning disabilities are more intelligent than an average child. Learning disabilities vary from child to child. One child with LD may not have the same kind of learning problems as another child with LD. There is no cure for learning disabilities and they are life-long. However, children with LD can be high achievers and can be taught ways to get around the learning disability. In this research work, data mining using machine learning techniques are used to analyze the symptoms of LD, establish interrelationships between them and evaluate the relative importance of these symptoms. To increase the diagnostic accuracy of learning disability prediction, a knowledge based tool based on statistical machine learning or data mining techniques, with high accuracy,according to the knowledge obtained from the clinical information, is proposed. The basic idea of the developed knowledge based tool is to increase the accuracy of the learning disability assessment and reduce the time used for the same. Different statistical machine learning techniques in data mining are used in the study. Identifying the important parameters of LD prediction using the data mining techniques, identifying the hidden relationship between the symptoms of LD and estimating the relative significance of each symptoms of LD are also the parts of the objectives of this research work. The developed tool has many advantages compared to the traditional methods of using check lists in determination of learning disabilities. For improving the performance of various classifiers, we developed some preprocessing methods for the LD prediction system. A new system based on fuzzy and rough set models are also developed for LD prediction. Here also the importance of pre-processing is studied. A Graphical User Interface (GUI) is designed for developing an integrated knowledge based tool for prediction of LD as well as its degree. The designed tool stores the details of the children in the student database and retrieves their LD report as and when required. The present study undoubtedly proves the effectiveness of the tool developed based on various machine learning techniques. It also identifies the important parameters of LD and accurately predicts the learning disability in school age children. This thesis makes several major contributions in technical, general and social areas. The results are found very beneficial to the parents, teachers and the institutions. They are able to diagnose the child’s problem at an early stage and can go for the proper treatments/counseling at the correct time so as to avoid the academic and social losses.

Document Image Segmentation and Compression using Artificial Neural Networks and Evolutionary Methods

The work is intended to study the following important aspects of document image processing and develop new methods. (1) Segmentation ofdocument images using adaptive interval valued neuro-fuzzy method. (2) Improving the segmentation procedure using Simulated Annealing technique. (3) Development of optimized compression algorithms using Genetic Algorithm and parallel Genetic Algorithm (4) Feature extraction of document images (5) Development of IV fuzzy rules. This work also helps for feature extraction and foreground and background identification. The proposed work incorporates Evolutionary and hybrid methods for segmentation and compression of document images. A study of different neural networks used in image processing, the study of developments in the area of fuzzy logic etc is carried out in this work

“Improved Feature Extraction and Classification Techniques for Multispectral Brain Magnetic Resonance Images”

Magnetic Resonance Imaging (MRI) is a multi sequence medical imaging technique in which stacks of images are acquired with different tissue contrasts. Simultaneous observation and quantitative analysis of normal brain tissues and small abnormalities from these large numbers of different sequences is a great challenge in clinical applications. Multispectral MRI analysis can simplify the job considerably by combining unlimited number of available co-registered sequences in a single suite. However, poor performance of the multispectral system with conventional image classification and segmentation methods makes it inappropriate for clinical analysis. Recent works in multispectral brain MRI analysis attempted to resolve this issue by improved feature extraction approaches, such as transform based methods, fuzzy approaches, algebraic techniques and so forth. Transform based feature extraction methods like Independent Component Analysis (ICA) and its extensions have been effectively used in recent studies to improve the performance of multispectral brain MRI analysis. However, these global transforms were found to be inefficient and inconsistent in identifying less frequently occurred features like small lesions, from large amount of MR data. The present thesis focuses on the improvement in ICA based feature extraction techniques to enhance the performance of multispectral brain MRI analysis. Methods using spectral clustering and wavelet transforms are proposed to resolve the inefficiency of ICA in identifying small abnormalities, and problems due to ICA over-completeness. Effectiveness of the new methods in brain tissue classification and segmentation is confirmed by a detailed quantitative and qualitative analysis with synthetic and clinical, normal and abnormal, data. In comparison to conventional classification techniques, proposed algorithms provide better performance in classification of normal brain tissues and significant small abnormalities.

classification and content based retrieval of digital mammograms and placental sonograms

Image processing has been a challenging and multidisciplinary research area since decades with continuing improvements in its various branches especially Medical Imaging. The healthcare industry was very much benefited with the advances in Image Processing techniques for the efficient management of large volumes of clinical data. The popularity and growth of Image Processing field attracts researchers from many disciplines including Computer Science and Medical Science due to its applicability to the real world. In the meantime, Computer Science is becoming an important driving force for the further development of Medical Sciences. The objective of this study is to make use of the basic concepts in Medical Image Processing and develop methods and tools for clinicians’ assistance. This work is motivated from clinical applications of digital mammograms and placental sonograms, and uses real medical images for proposing a method intended to assist radiologists in the diagnostic process. The study consists of two domains of Pattern recognition, Classification and Content Based Retrieval. Mammogram images of breast cancer patients and placental images are used for this study. Cancer is a disaster to human race. The accuracy in characterizing images using simplified user friendly Computer Aided Diagnosis techniques helps radiologists in detecting cancers at an early stage. Breast cancer which accounts for the major cause of cancer death in women can be fully cured if detected at an early stage. Studies relating to placental characteristics and abnormalities are important in foetal monitoring. The diagnostic variability in sonographic examination of placenta can be overlooked by detailed placental texture analysis by focusing on placental grading. The work aims on early breast cancer detection and placental maturity analysis. This dissertation is a stepping stone in combing various application domains of healthcare and technology.

A Data Mining Approach for the Identification of Adverse Drug Events (ADE) resulting from Drug-Drug Interactions (DDI) to improve pharmacovigilance

In the current study, epidemiology study is done by means of literature survey in groups identified to be at higher potential for DDIs as well as in other cases to explore patterns of DDIs and the factors affecting them. The structure of the FDA Adverse Event Reporting System (FAERS) database is studied and analyzed in detail to identify issues and challenges in data mining the drug-drug interactions. The necessary pre-processing algorithms are developed based on the analysis and the Apriori algorithm is modified to suit the process. Finally, the modules are integrated into a tool to identify DDIs. The results are compared using standard drug interaction database for validation. 31% of the associations obtained were identified to be new and the match with existing interactions was 69%. This match clearly indicates the validity of the methodology and its applicability to similar databases. Formulation of the results using the generic names expanded the relevance of the results to a global scale. The global applicability helps the health care professionals worldwide to observe caution during various stages of drug administration thus considerably enhancing pharmacovigilance

A Novel Decision Tree Algorithm for Numeric Datasets - C 4.5*Stat

Decision trees are very powerful tools for classification in data mining tasks that involves different types of attributes. When coming to handling numeric data sets, usually they are converted first to categorical types and then classified using information gain concepts. Information gain is a very popular and useful concept which tells you, whether any benefit occurs after splitting with a given attribute as far as information content is concerned. But this process is computationally intensive for large data sets. Also popular decision tree algorithms like ID3 cannot handle numeric data sets. This paper proposes statistical variance as an alternative to information gain as well as statistical mean to split attributes in completely numerical data sets. The new algorithm has been proved to be competent with respect to its information gain counterpart C4.5 and competent with many existing decision tree algorithms against the standard UCI benchmarking datasets using the ANOVA test in statistics. The specific advantages of this proposed new algorithm are that it avoids the computational overhead of information gain computation for large data sets with many attributes, as well as it avoids the conversion to categorical data from huge numeric data sets which also is a time consuming task. So as a summary, huge numeric datasets can be directly submitted to this algorithm without any attribute mappings or information gain computations. It also blends the two closely related fields statistics and data mining

Speech Recognition of Malayalam Numbers

Digit speech recognition is important in many applications such as automatic data entry, PIN entry, voice dialing telephone, automated banking system, etc. This paper presents speaker independent speech recognition system for Malayalam digits. The system employs Mel frequency cepstrum coefficient (MFCC) as feature for signal processing and Hidden Markov model (HMM) for recognition. The system is trained with 21 male and female voices in the age group of 20 to 40 years and there was 98.5% word recognition accuracy (94.8% sentence recognition accuracy) on a test set of continuous digit recognition task.

Handwritten Character Recognition of South Indian Scripts: A Review

Handwritten character recognition is always a frontier area of research in the field of pattern recognition and image processing and there is a large demand for OCR on hand written documents. Even though, sufficient studies have performed in foreign scripts like Chinese, Japanese and Arabic characters, only a very few work can be traced for handwritten character recognition of Indian scripts especially for the South Indian scripts. This paper provides an overview of offline handwritten character recognition in South Indian Scripts, namely Malayalam, Tamil, Kannada and Telungu

Significance Of Classification Techniques In Prediction Of Learning Disabilities

The aim of this study is to show the importance of two classification techniques, viz. decision tree and clustering, in prediction of learning disabilities (LD) of school-age children. LDs affect about 10 percent of all children enrolled in schools. The problems of children with specific learning disabilities have been a cause of concern to parents and teachers for some time. Decision trees and clustering are powerful and popular tools used for classification and prediction in Data mining. Different rules extracted from the decision tree are used for prediction of learning disabilities. Clustering is the assignment of a set of observations into subsets, called clusters, which are useful in finding the different signs and symptoms (attributes) present in the LD affected child. In this paper, J48 algorithm is used for constructing the decision tree and K-means algorithm is used for creating the clusters. By applying these classification techniques, LD in any child can be identified

Computing median and antimedian sets in median graphs

The median (antimedian) set of a profile π = (u1, . . . , uk) of vertices of a graphG is the set of vertices x that minimize (maximize) the remoteness i d(x,ui ). Two algorithms for median graphs G of complexity O(nidim(G)) are designed, where n is the order and idim(G) the isometric dimension of G. The first algorithm computes median sets of profiles and will be in practice often faster than the other algorithm which in addition computes antimedian sets and remoteness functions and works in all partial cubes