An Introduction to Random Sets

The study of random sets is a large and rapidly growing area with connections to many areas of mathematics and applications in widely varying disciplines, from economics and decision theory to biostatistics and image analysis. The drawback to such diversity is that the research reports are scattered throughout the literature, with the result that in science and engineering, and even in the statistics community, the topic is not well known and much of the enormous potential of random sets remains untapped. An Introduction to Random Sets provides a friendly but solid initiation into the theory of random sets. It builds the foundation for studying random set data, which, viewed as imprecise or incomplete observations, are ubiquitous in today's technological society. The author, widely known for his best-selling A First Course in Fuzzy Logic text as well as his pioneering work in random sets, explores motivations, such as coarse data analysis and uncertainty analysis in intelligent systems, for studying random sets as stochastic models. Other topics include random closed sets, related uncertainty measures, the Choquet integral, the convergence of capacity functionals, and the statistical framework for set-valued observations. An abundance of examples and exercises reinforce the concepts discussed. Designed as a textbook for a course at the advanced undergraduate or beginning graduate level, this book will serve equally well for self-study and as a reference for researchers in fields such as statistics, mathematics, engineering, and computer science.

Science & Math

Nguyen, Hung T.

Mathematics

Chapman and Hall/CRC

This is the first half of a text for a two semester course in mathematical statistics at the senior/graduate level for those who need a strong background in statistics as an essential tool in their career. To study this text, the reader needs a thorough familiarity with calculus including such things as Jacobians and series but somewhat less intense familiarity with matrices including quadratic forms and eigenvalues. For convenience, these lecture notes were divided into two parts: Volume I, Probability for Statistics, for the first semester, and Volume II, Statistical Inference, for the second. We suggest that the following distinguish this text from other introductions to mathematical statistics. 1. The most obvious thing is the layout. We have designed each lesson for the (U.S.) 50 minute class; those who study independently probably need the traditional three hours for each lesson. Since we have more than (the U.S. again) 90 lessons, some choices have to be made. In the table of contents, we have used a * to designate those lessons which are "interesting but not essential" (INE) and may be omitted from a general course; some exercises and proofs in other lessons are also "INE". We have made lessons of some material which other writers might stuff into appendices. Incorporating this freedom of choice has led to some redundancy, mostly in definitions, which may be beneficial.

Fundamentals of Mathematical Statistics: Probability for Statistics (Springer Texts in Statistics)

Rogers, Gerald S.

Springer

Uncertainty Models for Knowledge-Based Systems: A Unified Approach to the Measurement of Uncertainty

Computers & Technology

Goodman, Irwin R.

Computer Science

Elsevier Science Ltd.

This volume contains the most significant papers written by L. A. Zadeh, who in 1965 introduced the concept of a fuzzy set. Fuzzy set theory has become the foundation for the development of the fields of artificial intelligence and expert systems, especially in the applications of knowledge-based systems. As such, Zadeh's work has influenced researchers around the world. Zadeh has cooperated with editors in choosing the papers presented here, and the editors have provided an introduction for each paper. Topics covered include probability measures of fuzzy events, similarity relations and fuzzy orderings, a fuzzy-algorithmic approach to the definition of complex or imprecise concepts, and much more.

Fuzzy Sets and Applications: Selected Papers by Lotfi A. Zadeh

Tong, Richard M.

Wiley-Interscience

The second edition of the popular A First Course in Fuzzy Logic will continue to provide the ideal introduction to the theory and applications of fuzzy logic. The authors provide a firm mathematical basis for the calculus of fuzzy concepts-necessary to design intelligent systems-and give the student a solid background for further studies and real-world applications. This new edition provides many new exercises designed to enhance the reader's understanding of the concepts. The authors have expanded on the algebra background needed for the more advanced topics, and include significant new material on basic connectives and the algebraic properties of fuzzy logic, rough sets, conditional events, distributions of random sets, and derivatives of fuzzy measures. With its comprehensive updates, A First Course in Fuzzy Logic, Second Edition presents all the background necessary for students to begin using fuzzy logic in its many-and rapidly growing-applications.

A First Course in Fuzzy Logic, Second Edition

Walker, Elbert A.

CRC-Press

This collection compiles the seminal contributions of Michio Sugeno on fuzzy systems and technologies. Fuzzy Modeling &amp; Control: Selected Works of Sugeno serves as a singular resource that provides a clear, comprehensive treatment of fuzzy control systems. The book comprises two parts 
<li>fuzzy system identification and modeling 
</li>
<li>systems control Each part outlines the fundamentals of fuzzy logic and covers essential material for understanding the mathematical and modeling details in Sugeno's works. Introductory chapters include extended summaries of each paper or group of papers, suggesting where the theories discussed might be useful in application.</li>

Fuzzy Modeling and Control: Selected Works of Sugeno

Prasad, Nadipuram R.

A First Course in Fuzzy Logic (Textbooks in Mathematics)

A First Course in Fuzzy Logic, Fourth Edition is an expanded version of the successful third edition. It provides a comprehensive introduction to the theory and applications of fuzzy logic. This popular text offers a firm mathematical basis for the calculus of fuzzy concepts necessary for designing intelligent systems and a solid background for readers to pursue further studies and real-world applications. New in the Fourth Edition: <ul> <li style="list-style: none"> </li> <li>Features new results on fuzzy sets of type-2</li> <li style="list-style: none"> </li> <li>Provides more information on copulas for modeling dependence structures</li> <li style="list-style: none"> </li> <li>Includes quantum probability for uncertainty modeling in social sciences, especially in economics</li> <li style="list-style: none"> </li> </ul> With its comprehensive updates, this new edition presents all the background necessary for students, instructors and professionals to begin using fuzzy logic in its many--applications in computer science, mathematics, statistics, and engineering. About the Authors: Hung T. Nguyen is a Professor Emeritus at the Department of Mathematical Sciences, New Mexico State University. He is also an Adjunct Professor of Economics at Chiang Mai University, Thailand. Carol L. Walker is also a Professor Emeritus at the Department of Mathematical Sciences, New Mexico State University. Elbert A. Walker is a Professor Emeritus, Department of Mathematical Sciences, New Mexico State University.

Walker, Carol

Stochastic Dominance and Applications to Finance, Risk and Economics

Drawing from many sources in the literature, Stochastic Dominance and Applications to Finance, Risk and Economics illustrates how stochastic dominance (SD) can be used as a method for risk assessment in decision making. It provides basic background on SD for various areas of applications.  Useful Concepts and Techniques for Economics Applications  The majority of the text presents a systematic exposition of SD, emphasizing rigor and generality. It covers utility theory, multivariate SD, quantile functions, risk modeling, Choquet integrals, other risk measures, statistical inference, nonparametric estimation, hypothesis testing, and econometrics. The remainder of the book explores new applications of SD in finance, risk, and economics. At the beginning of each economic concept, the authors clearly explain only the necessary mathematics so readers are not overburdened with learning nonessential, arduous mathematics.  This accessible guide helps readers build a useful repertoire of mathematical tools in decision making under uncertainty, especially in investment science. It provides thorough coverage on the theory of SD, along with many applications to economics and other fields where risk is crucial.

Business & Money

Sriboonchita, Songsak

Wong, Wing-Keung

Dhompongsa, Sompong

Economics

A First Course in Fuzzy Logic, Fourth Edition is an expanded version of the successful third edition. It provides a comprehensive introduction to the theory and applications of fuzzy logic. This popular text offers a firm mathematical basis for the calculus of fuzzy concepts necessary for designing intelligent systems and a solid background for readers to pursue further studies and real-world applications. New in the Fourth Edition: <ul>
<li>Features new results on fuzzy sets of type-2</li> <li>Provides more information on copulas for modeling dependence structures</li> <li>Includes quantum probability for uncertainty modeling in social sciences, especially in economics</li> </ul> With its comprehensive updates, this new edition presents all the background necessary for students, instructors and professionals to begin using fuzzy logic in its many―applications in computer science, mathematics, statistics, and engineering. About the Authors: Hung T. Nguyen is a Professor Emeritus at the Department of Mathematical Sciences, New Mexico State University. He is also an Adjunct Professor of Economics at Chiang Mai University, Thailand. Carol L. Walker is also a Professor Emeritus at the Department of Mathematical Sciences, New Mexico State University. Elbert A. Walker is a Professor Emeritus, Department of Mathematical Sciences, New Mexico State University.

See the best price to sell, buy, or rent books by Nguyen, Hung T.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Nguyen, Hung T.

See the best price to sell, buy, or rent books by Nguyen, Hung T.. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

An Introduction to Random Sets

Fundamentals of Mathematical Statistics: Probability for Statistics (Springer Texts in Statistics)

Uncertainty Models for Knowledge-Based Systems: A Unified Approach to the Measurement of Uncertainty

Fuzzy Sets and Applications: Selected Papers by Lotfi A. Zadeh

A First Course in Fuzzy Logic, Second Edition

Fuzzy Modeling and Control: Selected Works of Sugeno

A First Course in Fuzzy Logic (Textbooks in Mathematics)

Stochastic Dominance and Applications to Finance, Risk and Economics

A First Course in Fuzzy Logic (Textbooks in Mathematics)

Stochastic Dominance and Applications to Finance, Risk and Economics