Fuzzy Sequential Analysis


Book Description

In the four decades since its inception, the theory of fuzzyness has matured into wide ranging of collection of concepts and techniques for dealing with complex phenomenon which do not lend themselves to analysis by classical methods based on probability theory bivalent logic. Sequential analysis is a method of statistical inference whose characteristic feature is that the number of observations required by the procedure is not determined in advance of the experiment. Decision making in classical statistical inference is based on crispness of data, random variables, exact hypotheses and decision rules. But there are many different situations in which the above asuumptions are not sufficient to address the problems.In this book, different sequential inference procedures have been addressed for fuzzy observations. The articles included in this book are of theoretical in nature, where the effect of fuzzification on the sequential inference procedures, under consideration, have been studied.Each chapter of this book have published as research paper in different reputed journals all over the world.




Sequence Analysis and Related Approaches


Book Description

This open access book provides innovative methods and original applications of sequence analysis (SA) and related methods for analysing longitudinal data describing life trajectories such as professional careers, family paths, the succession of health statuses, or the time use. The applications as well as the methodological contributions proposed in this book pay special attention to the combined use of SA and other methods for longitudinal data such as event history analysis, Markov modelling, and sequence network. The methodological contributions in this book include among others original propositions for measuring the precarity of work trajectories, Markov-based methods for clustering sequences, fuzzy and monothetic clustering of sequences, network-based SA, joint use of SA and hidden Markov models, and of SA and survival models. The applications cover the comparison of gendered occupational trajectories in Germany, the study of the changes in women market participation in Denmark, the study of typical day of dual-earner couples in Italy, of mobility patterns in Togo, of internet addiction in Switzerland, and of the quality of employment career after a first unemployment spell. As such this book provides a wealth of information for social scientists interested in quantitative life course analysis, and all those working in sociology, demography, economics, health, psychology, social policy, and statistics.; Provides new perspectives and methods for sequence analysis Focusses on the link between sequence analysis and other methods for longitudinal data, especially event history analysis and Markov models Stresses the complementarity of sequence analysis and other models for longitudinal data Applications of sequence analysis in a whole range of different domains This work was published by Saint Philip Street Press pursuant to a Creative Commons license permitting commercial use. All rights not granted by the work's license are retained by the author or authors.







Social Sequence Analysis


Book Description

Social sequence analysis includes a diverse and rapidly growing body of methods that social scientists have developed to help study complex ordered social processes, including chains of transitions, trajectories and other ordered phenomena. Social sequence analysis is not limited by content or time scale and can be used in many different fields, including sociology, communication, information science and psychology. Social Sequence Analysis aims to bring together both foundational and recent theoretical and methodological work on social sequences from the last thirty years. A unique reference book for a new generation of social scientists, this book will aid demographers who study life-course trajectories and family histories, sociologists who study career paths or work/family schedules, communication scholars and micro-sociologists who study conversation, interaction structures and small-group dynamics, as well as social epidemiologists.




Vague Data Analysis Using Sequential Test


Book Description

The existing sequential test using Bernoulli distribution can only be applied when no uncertainty/indeterminacy is found in testing the hypothesis. This paper introduces neutrosophic Bernoulli distribution and sequential test using the distribution. The operational procedure of the proposed test will be introduced and applied for testing the hypothesis in the presence of uncertainty.




Madan Lal Puri Selected Collected Works


Book Description

Professor Puri is one of the most versatile and prolific researchers in the world in mathematical statistics. His research areas include nonparametric statistics, order statistics, limit theory under mixing, time series, splines, tests of normality, generalized inverses of matrices and related topics, stochastic processes, statistics of directional data, random sets, and fuzzy sets and fuzzy measures. His fundamental contributions in developing new rank-based methods and precise evaluation of the standard procedures, asymptotic expansions of distributions of rank statistics, as well as large deviation results concerning them, span such areas as analysis of variance, analysis of covariance, multivariate analysis, and time series, to mention a few. His in-depth analysis has resulted in pioneering research contributions to prominent journals that have substantial impact on current research. This book together with the other two volumes (Volume 1: Nonparametric Methods in Statistics and Related Topics; Volume 2: Probability Theory and Extreme Value Theory), are a concerted effort to make his research works easily available to the research community. The sheer volume of the research output by him and his collaborators, coupled with the broad spectrum of the subject matters investigated, and the great number of outlets where the papers were published, attach special significance in making these works easily accessible. The papers selected for inclusion in this work have been classified into three volumes each consisting of several parts. All three volumes carry a final part consisting of the contents of the other two, as well as the complete list of Professor Puri's publications.




Time Series, Fuzzy Analysis and Miscellaneous Topics


Book Description

Professor Puri is one of the most versatile and prolific researchers in the world in mathematical statistics. His research areas include nonparametric statistics, order statistics, limit theory under mixing, time series, splines, tests of normality, generalized inverses of matrices and related topics, stochastic processes, statistics of directional data, random sets, and fuzzy sets and fuzzy measures. His fundamental contributions in developing new rank-based methods and precise evaluation of the standard procedures, asymptotic expansions of distributions of rank statistics, as well as large deviation results concerning them, span such areas as analysis of variance, analysis of covariance, multivariate analysis, and time series, to mention a few. His in-depth analysis has resulted in pioneering research contributions to prominent journals that have substantial impact on current research.This book together with the other two volumes (Volume 1: Nonparametric Methods in Statistics and Related Topics; Volume 2: Probability Theory and Extreme Value Theory), are a concerted effort to make his research works easily available to the research community. The sheer volume of the research output by him and his collaborators, coupled with the broad spectrum of the subject matters investigated, and the great number of outlets where the papers were published, attach special significance in making these works easily accessible.The papers selected for inclusion in this work have been classified into three volumes each consisting of several parts. All three volumes carry a final part consisting of the contents of the other two, as well as the complete list of Professor Puri's publications.




Sequence Analysis and Related Approaches


Book Description

This open access book provides innovative methods and original applications of sequence analysis (SA) and related methods for analysing longitudinal data describing life trajectories such as professional careers, family paths, the succession of health statuses, or the time use. The applications as well as the methodological contributions proposed in this book pay special attention to the combined use of SA and other methods for longitudinal data such as event history analysis, Markov modelling, and sequence network. The methodological contributions in this book include among others original propositions for measuring the precarity of work trajectories, Markov-based methods for clustering sequences, fuzzy and monothetic clustering of sequences, network-based SA, joint use of SA and hidden Markov models, and of SA and survival models. The applications cover the comparison of gendered occupational trajectories in Germany, the study of the changes in women market participation in Denmark, the study of typical day of dual-earner couples in Italy, of mobility patterns in Togo, of internet addiction in Switzerland, and of the quality of employment career after a first unemployment spell. As such this book provides a wealth of information for social scientists interested in quantitative life course analysis, and all those working in sociology, demography, economics, health, psychology, social policy, and statistics.




Rough-Fuzzy Pattern Recognition


Book Description

Learn how to apply rough-fuzzy computing techniques to solve problems in bioinformatics and medical image processing Emphasizing applications in bioinformatics and medical image processing, this text offers a clear framework that enables readers to take advantage of the latest rough-fuzzy computing techniques to build working pattern recognition models. The authors explain step by step how to integrate rough sets with fuzzy sets in order to best manage the uncertainties in mining large data sets. Chapters are logically organized according to the major phases of pattern recognition systems development, making it easier to master such tasks as classification, clustering, and feature selection. Rough-Fuzzy Pattern Recognition examines the important underlying theory as well as algorithms and applications, helping readers see the connections between theory and practice. The first chapter provides an introduction to pattern recognition and data mining, including the key challenges of working with high-dimensional, real-life data sets. Next, the authors explore such topics and issues as: Soft computing in pattern recognition and data mining A mathematical framework for generalized rough sets, incorporating the concept of fuzziness in defining the granules as well as the set Selection of non-redundant and relevant features of real-valued data sets Selection of the minimum set of basis strings with maximum information for amino acid sequence analysis Segmentation of brain MR images for visualization of human tissues Numerous examples and case studies help readers better understand how pattern recognition models are developed and used in practice. This text—covering the latest findings as well as directions for future research—is recommended for both students and practitioners working in systems design, pattern recognition, image analysis, data mining, bioinformatics, soft computing, and computational intelligence.




Statistical Methods for Fuzzy Data


Book Description

Statistical data are not always precise numbers, or vectors, or categories. Real data are frequently what is called fuzzy. Examples where this fuzziness is obvious are quality of life data, environmental, biological, medical, sociological and economics data. Also the results of measurements can be best described by using fuzzy numbers and fuzzy vectors respectively. Statistical analysis methods have to be adapted for the analysis of fuzzy data. In this book, the foundations of the description of fuzzy data are explained, including methods on how to obtain the characterizing function of fuzzy measurement results. Furthermore, statistical methods are then generalized to the analysis of fuzzy data and fuzzy a-priori information. Key Features: Provides basic methods for the mathematical description of fuzzy data, as well as statistical methods that can be used to analyze fuzzy data. Describes methods of increasing importance with applications in areas such as environmental statistics and social science. Complements the theory with exercises and solutions and is illustrated throughout with diagrams and examples. Explores areas such quantitative description of data uncertainty and mathematical description of fuzzy data. This work is aimed at statisticians working with fuzzy logic, engineering statisticians, finance researchers, and environmental statisticians. It is written for readers who are familiar with elementary stochastic models and basic statistical methods.