Linear Models in the Mathematics of Uncertainty

The purpose of this book is to present new mathematical techniques for modeling global issues. These mathematical techniques are used to determine linear equations between a dependent variable and one or more independent variables in cases where standard

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John N. Mordeson, Mark J. Wierman, Terry D. Clark, Alex Pham, and Michael A. Redmond

Linear Models in the Mathematics of Uncertainty

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Authors John N. Mordeson Department of Mathematics Creighton University Omaha USA

Alex Pham Department of Mathematics Creighton University Omaha USA

Mark J. Wierman Department of Computer Science Creighton University Omaha USA

Michael A. Redmond Department of Mathematics Creighton University Omaha USA

Terry D. Clark Department of Political Science Creighton University Omaha USA

ISSN 1860-949X e-ISSN 1860-9503 ISBN 978-3-642-35223-2 e-ISBN 978-3-642-35224-9 DOI 10.1007/978-3-642-35224-9 Springer Heidelberg New York Dordrecht London Library of Congress Control Number: 2012953004 c Springer-Verlag Berlin Heidelberg 2013  This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. Exempted from this legal reservation are brief excerpts in connection with reviews or scholarly analysis or material supplied specifically for the purpose of being entered and executed on a computer system, for exclusive use by the purchaser of the work. Duplication of this publication or parts thereof is permitted only under the provisions of the Copyright Law of the Publisher’s location, in its current version, and permission for use must always be obtained from Springer. Permissions for use may be obtained through RightsLink at the Copyright Clearance Center. Violations are liable to prosecution under the respective Copyright Law. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. While the advice and information in this book are believed to be true and accurate at the date of publication, neither the authors nor the editors nor the publisher can accept any legal responsibility for any errors or omissions that may be made. The publisher makes no warranty, express or implied, with respect to the material contained herein. Printed on acid-free paper Springer is part of Springer Science+Business Media (www.springer.com)

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In the soft sciences, imprecision, uncertainty, incompleteness of information and partiality of truth lie in the center rather than on the periphery in the construction of models. Lotfi Zadeh

Albert Einstein stated that development of Western science is based on two great achievements: • the invention of the formal logical system, and • the discovery of the p