Fuzzy linear programming is an application of fuzzy set theory in linear decision making problems and most of these problems are related to linear programming (LP) with fuzzy variables. This book contains an approximate but convenient method, without using the ranking functions, for solving these problems with fuzzy non-negative technical coefficients. The method has been illustrated with numerical examples.

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As the Solutions Manual, this book is meant to accompany the main title, Introduction to Linear Regression Analysis, Fifth Edition. Clearly balancing theory with applications, this book describes both the conventional and less common uses of linear regression in the practical context of today's mathematical and scientific research. Beginning with a general introduction to regression modeling, including typical applications, the book then outlines a host of technical tools that form the linear regression analytical arsenal, including: basic inference procedures and introductory aspects of model adequacy checking; how transformations and weighted least squares can be used to resolve problems of model inadequacy; how to deal with influential observations; and polynomial regression models and their variations. The book also includes material on regression models with autocorrelated errors, bootstrapping regression estimates, classification and regression trees, and regression model validation.

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This book points out to logistic regression analysis in fuzzy environment. In this regard, three clinical situations are considered with a proposed method for each one. First and second methods model fuzzy diagnosis based on a set of non fuzzy (crisp) variables by using a real number and a fuzzy number for the possibility of being ill, respectively. The third model is proposed for a situation of no ambiguities in diagnosis but in the relations among the variables.

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Praise for the Third Edition «…this is an excellent book which could easily be used as a course text…» —International Statistical Institute The Fourth Edition of Applied Linear Regression provides a thorough update of the basic theory and methodology of linear regression modeling. Demonstrating the practical applications of linear regression analysis techniques, the Fourth Edition uses interesting, real-world exercises and examples. Stressing central concepts such as model building, understanding parameters, assessing fit and reliability, and drawing conclusions, the new edition illustrates how to develop estimation, confidence, and testing procedures primarily through the use of least squares regression. While maintaining the accessible appeal of each previous edition,Applied Linear Regression, Fourth Edition features: Graphical methods stressed in the initial exploratory phase, analysis phase, and summarization phase of an analysis In-depth coverage of parameter estimates in both simple and complex models, transformations, and regression diagnostics Newly added material on topics including testing, ANOVA, and variance assumptions Updated methodology, such as bootstrapping, cross-validation binomial and Poisson regression, and modern model selection methods Applied Linear Regression, Fourth Edition is an excellent textbook for upper-undergraduate and graduate-level students, as well as an appropriate reference guide for practitioners and applied statisticians in engineering, business administration, economics, and the social sciences.

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In the Present Book Chapter - I is an introductory one. It contains the general introduction about the problem of testing linear restrictions on the parameters of the linear regression models, Chapter - II describes the concept and the estimation of parameters of linear model subject to the linear restrictions. Chapter - III deals with the review about the various tests for linear restrictions in the linear statistical models including Wald, Likelihood Ratio and Lagrange Multiplier tests. Chapter - IV gives the details about the various problems of testing equality between sets of regression coefficients in linear regression models, Chapter - V proposes some new criteria for testing linear restrictions on parameters in linear statistical models. Chapter - VI presents the conclusions. Several selected references for the present research work have been given under the title "BIBLIOGRAPHY".

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This book deals with a concise study of convergence in intuitionistic fuzzy n-normed linear spaces. This book mainly contains the author's own research work in the area of lacunary ideal convergence. Fuzzy normed spaces have been an increasingly popular area of mathematical research in recent times, both in terms of theory and applications. But the availability of books in the area of fuzzy normed spaces is very rare. This book provides a good discussion on the development of both fuzzy and intuitionistic fuzzy set theory. The transition from fuzzy normed linear spaces to intuitionistic fuzzy n-normed linear spaces has been presented systematically. Anybody interested in the theory or application of fuzzy or intuitionistic fuzzy normed spaces will find this book more than useful. The book is written in such a way that mathematical prerequisites are minimum. Since the main subject of study in this book is a generalisaton of the concept of usual convergence, so all the related results in convergence have been incorporated in the book. This book may be used as a ready reference for an up to date account of results in the theory of fuzzy/intuitionistic fuzzy normed linear spaces.

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Linear programming is one of the most frequently applied operations research techniques. The classical tool for solving the linear programming problem in practice is the class of simplex algorithm which was proposed and developed by Dantzig. A lot of real world decision problems are described by linear programming models and sometimes it is necessary to formulate them with elements of imprecision or uncertainty. This imprecise nature has long been studied with the help of the probability theory. However, the probability theory might not provide the correct interpretation to solve some practical decision making problems. In these cases, the fuzzy set theory might be more helpful. In this book, the limitations and shortcomings of existing methods for solving linear programming problems with fuzzy sets are pointed out. Some new ranking approaches for the ordering of fuzzy sets and vague sets are developed and also new methods to find the unique optimal solutions of linear programming problems under fuzzy environment and vague environment are presented.

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Praise for the Fourth Edition «As with previous editions, the authors have produced a leading textbook on regression.» —Journal of the American Statistical Association A comprehensive and up-to-date introduction to the fundamentals of regression analysis Introduction to Linear Regression Analysis, Fifth Edition continues to present both the conventional and less common uses of linear regression in today’s cutting-edge scientific research. The authors blend both theory and application to equip readers with an understanding of the basic principles needed to apply regression model-building techniques in various fields of study, including engineering, management, and the health sciences. Following a general introduction to regression modeling, including typical applications, a host of technical tools are outlined such as basic inference procedures, introductory aspects of model adequacy checking, and polynomial regression models and their variations. The book then discusses how transformations and weighted least squares can be used to resolve problems of model inadequacy and also how to deal with influential observations. The Fifth Edition features numerous newly added topics, including: A chapter on regression analysis of time series data that presents the Durbin-Watson test and other techniques for detecting autocorrelation as well as parameter estimation in time series regression models Regression models with random effects in addition to a discussion on subsampling and the importance of the mixed model Tests on individual regression coefficients and subsets of coefficients Examples of current uses of simple linear regression models and the use of multiple regression models for understanding patient satisfaction data. In addition to Minitab, SAS, and S-PLUS, the authors have incorporated JMP and the freely available R software to illustrate the discussed techniques and procedures in this new edition. Numerous exercises have been added throughout, allowing readers to test their understanding of the material. Introduction to Linear Regression Analysis, Fifth Edition is an excellent book for statistics and engineering courses on regression at the upper-undergraduate and graduate levels. The book also serves as a valuable, robust resource for professionals in the fields of engineering, life and biological sciences, and the social sciences.

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In the book an attempt has been made to develop some new diagnostic tests for statistical model building in the context of linear regression models. Diagnostics of outliers has been described and a test for identifying outliers by using predicted residuals has been proposed in the present study. Besides outliers, a measure of influence for diagnostics has been developed in the study. Some new modified R2 and criteria for model selection have been developed along with modified mean square prediction error criteria; and modified information criteria for model selection. A test for exogeneity in model specification by using augmented regression model; and a test for stability of regression parameters in model specification have been proposed under diagnostic tests. A new test for misspecification of the linear regression model has been derived along with a modified Rainbow Test by using Internally studentized residuals. The problem of misspecification of non-nested linear regression models, has been discussed together with a diagnostic test for functional form between loglinear and linear regression models.

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We consider semiparametric regression model where the mean function of this model has two parts, the parametric is assumed to be linear function of p-dimensional covariates and nonparametric is assumed to be a smooth penalized spline. By using a convenient connection between penalized splines and mixed models, we can represent semiparametric regression model as a mixed model. Bayesian approach is employed to make inferences on the resulting mixed model coefficients, and we prove some theorems about posterior. We also investigate the large sample property of the Bayes factor for testing the polynomial component of spline model against the fully spline semiparametric alternative model, as well as Bayesian approach to semiparametric regression model which is described by using fuzzy sets and membership functions. The membership functions are interpreted as likelihood functions for the model, furthermore, we prove some theorems about posterior and Bayes factor in this case.

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Regression Analysis: Unified Concepts, Practical Applications, Computer Implementation is a concise and innovative book that gives a complete presentation of applied regression analysis in approximately one-half the space of competing books. With only the modest prerequisite of a basic (non-calculus) statistics course this text is appropriate for the widest possible audience including college juniors, seniors and first-year graduate students in business and statistics, as well as professionals in business and industry. The book is able to accommodate this wide audience because of the unique, integrative approach that is taken to the teaching of regression analysis. Whereas other regression books cover regression in four chapters, beginning with a statistical review, followed by chapters on simple linear regression, matrix algebra and multiple regression, this book introduces regression and covers both simple linear regression and multiple regression in single cohesive chapter. This is made possible through an efficient, integrative discussion of the two techniques. Additionally, in the same chapter (Chapter Two) basic statistical and matrix algebra concepts are introduced as needed In order to facilitate instruction. This approach avoids the needless repetition that is often found in longer treatments of the subject, while serving to bring a collective focus to students of widely varying mathematical backgrounds.

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Parametric linear programming is one of the advanced topics in operations research, where we can find the optimal solution when there are changes in many of the statements included in the model and continuously, which makes this subject of maximum importance when decision-makers, helping them to make the best decision. Also, fuzzy logic was employed in linear programming by many researchers, that the importance of the subject to the fact that the real data are often uncertain. This work created a link between these subjects by the name of fuzzy - parametric linear programming and applied in practice in the General Company for Electrical Industries to develop some products for the purpose of increasing profits by using the formula that helps to improve computational performance.

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In the Present Book Chapter-I is an introductory one. Chapter - II deals the various types of residuals discussed in the literature for the linear regression analysis. Different types of residuals such as OLS, BLUS, Recursive, Internally and Externally studentized, predicted, and weighted residuals have been explained with their properties. Chapter - III presents some new applications of residuals in linear regression models under the problem of heteroscedasticity.Chapter - IV proposes some criteria for testing the equality between sets of regression coefficients in two linear models under two different specifications of error variance using studentized residuals. Chapter - V depicts the conclusion of the present research study. Various selected references regarding present study have been documented under a separate title “BIBLIOGRAPHY”.

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Computational Intelligence: Synergies of Fuzzy Logic, Neural Networks and Evolutionary Computing presents an introduction to some of the cutting edge technological paradigms under the umbrella of computational intelligence. Computational intelligence schemes are investigated with the development of a suitable framework for fuzzy logic, neural networks and evolutionary computing, neuro-fuzzy systems, evolutionary-fuzzy systems and evolutionary neural systems. Applications to linear and non-linear systems are discussed with examples. Key features: Covers all the aspects of fuzzy, neural and evolutionary approaches with worked out examples, MATLAB® exercises and applications in each chapter Presents the synergies of technologies of computational intelligence such as evolutionary fuzzy neural fuzzy and evolutionary neural systems Considers real world problems in the domain of systems modelling, control and optimization Contains a foreword written by Lotfi Zadeh Computational Intelligence: Synergies of Fuzzy Logic, Neural Networks and Evolutionary Computing is an ideal text for final year undergraduate, postgraduate and research students in electrical, control, computer, industrial and manufacturing engineering.

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In this present book Chapter I is an introductory one. It contains the general introduction about the importance of hypotheses testing in econometrics. Chapter II deals with the inferential aspects of linear models. It describes the various problems of the theory of Econometrics. Chapter III describes the existing criteria for testing general linear hypotheses in the linear models. It contains the derivation and applications of Restricted Least Squares estimation in the theory of Econometrics.Chapter IV proposes same alternative criteria for testing general linear hypotheses in the generalized linear models. Mean Squared Error (MSE) criteria have been explained for testing general linear hypotheses in the generalized linear models under the problems of heteroscedasticity and singular linear models.Chapter V gives the conclusions of the book .Several relavant articles regarding the Hypotheses testing in linear regression models have been presented under a title ‘BIBLIOGRAPHY’

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Praise for the First Edition «The obvious enthusiasm of Myers, Montgomery, and Vining and their reliance on their many examples as a major focus of their pedagogy make Generalized Linear Models a joy to read. Every statistician working in any area of applied science should buy it and experience the excitement of these new approaches to familiar activities.» —Technometrics Generalized Linear Models: With Applications in Engineering and the Sciences, Second Edition continues to provide a clear introduction to the theoretical foundations and key applications of generalized linear models (GLMs). Maintaining the same nontechnical approach as its predecessor, this update has been thoroughly extended to include the latest developments, relevant computational approaches, and modern examples from the fields of engineering and physical sciences. This new edition maintains its accessible approach to the topic by reviewing the various types of problems that support the use of GLMs and providing an overview of the basic, related concepts such as multiple linear regression, nonlinear regression, least squares, and the maximum likelihood estimation procedure. Incorporating the latest developments, new features of this Second Edition include: A new chapter on random effects and designs for GLMs A thoroughly revised chapter on logistic and Poisson regression, now with additional results on goodness of fit testing, nominal and ordinal responses, and overdispersion A new emphasis on GLM design, with added sections on designs for regression models and optimal designs for nonlinear regression models Expanded discussion of weighted least squares, including examples that illustrate how to estimate the weights Illustrations of R code to perform GLM analysis The authors demonstrate the diverse applications of GLMs through numerous examples, from classical applications in the fields of biology and biopharmaceuticals to more modern examples related to engineering and quality assurance. The Second Edition has been designed to demonstrate the growing computational nature of GLMs, as SAS®, Minitab®, JMP®, and R software packages are used throughout the book to demonstrate fitting and analysis of generalized linear models, perform inference, and conduct diagnostic checking. Numerous figures and screen shots illustrating computer output are provided, and a related FTP site houses supplementary material, including computer commands and additional data sets. Generalized Linear Models, Second Edition is an excellent book for courses on regression analysis and regression modeling at the upper-undergraduate and graduate level. It also serves as a valuable reference for engineers, scientists, and statisticians who must understand and apply GLMs in their work.

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In this book we define some new methods to approximate a fuzzy function by fuzzy polynomials. Also by introducing some new distances we define the nearest approximations of a fuzzy number. In his book, the definition of fuzzy linear programming with fuzzy variables and a method for solving it according to a special class of ranking which is used to find the approximating polynomials as well as definition of the problem of approximation, are discussed. Then the approximation problem on triangular fuzzy numbers leads us to an approximating polynomial name eϕ-approximation and on the set of all fuzzy numbers, the approximation problem gives us the D-approximation and we present a method to find it, also the universal and SAF-approximations which are special cases of D-approximation are found in this book. Also two best approximations of a triangular valued fuzzy function on a set of points are defined and are computed. Furthermore a chapter contains an idea for computing the nearest approximation of a fuzzy number out of a particular subset of all fuzzy numbers.

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The control of uncertain non-linear plants is a challenging task. Adaptive Fuzzy Controllers have been applied widely for the control of such processes. The book discusses one particular approach to the fuzzy controllers. Adaptive Model Free Fuzzy Control is a goal oriented approach which tries to control the plant based on the information available without specifically modeling the plant. The prime objective of the controller is to reduce the control error. The book discusses two different model free control structures and their relative merits and de-merits. Four different fuzzy identification schemes have been discussed which can be used to train the controller parameters. The simulation results from both the controllers have been included to get a better understanding of the control performance. The cooling coil of an air handling unit is used for the realistic testing of the controllers.

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In the Present book Chapter I is an introductory one. It contains the general introduction about the problem of heteroscedasticity. Chapter II describes some aspects of linear models with their inferential problems. It deals with some basic statistical results about Gauss-Markov linear model besides the restricted least squares estimation and its application to the tests of general linear hypotheses. Chapter III presents a brief review on the existing estimation methods for linear models under the various specifications of heteroscedastic variances. Chapter IV deals with the analysis and examination of different types of residuals with their applications in the regression analysis. It also contains the restricted residuals in ‘Seemingly Unrelated Regression’ (SUR) systems. Chapter V proposes some new estimation procedures for linear models under heteroscedasticity. Chapter VI depicts the conclusions .Several references articles regarding the estimation for linear models under heteroscedasticity have been presented under a title “BIBLIOGRAPHY”.

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