Overview
- Clear and didactic book about Monte Carlo methods using random fuzzy numbers to obtain approximate solutions to fuzzy optimization problems
- Includes various solved problems such as fuzzy linear programming, fuzzy regression, fuzzy inventory control, fuzzy game theory, fuzzy queuing theory
Part of the book series: Studies in Fuzziness and Soft Computing (STUDFUZZ, volume 222)
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About this book
1. 1 Introduction The objective of this book is to introduce Monte Carlo methods to ?nd good approximate solutions to fuzzy optimization problems. Many crisp (nonfuzzy) optimization problems have algorithms to determine solutions. This is not true for fuzzy optimization. There are other things to discuss in fuzzy optimization, which we will do later onin the book, like? and < between fuzzy numbers since there will probably be fuzzy constraints, and how do we evaluate max/minZ for Z the fuzzy value of the objective function. This book is divided into four parts: (1) Part I is the Introduction containing Chapters 1-5; (2) Part II, Chapters 6-16, has the applications of our Monte Carlo method to obtain approximate solutions to fuzzy optimization problems; (3)PartIII,comprisingChapters17-27,outlinesour“un?nishedbusiness”which are fuzzy optimization problems for which we have not yet applied our Monte Carlomethodtoproduceapproximatesolutions;and(4)PartIVisoursummary, conclusions and future research. 1. 1. 1 Part I First we need to be familiar with fuzzy sets. All you need to know about fuzzy sets for this book comprises Chapter 2. For a beginning introduction to fuzzy sets and fuzzy logic see [2]. Three other items related to fuzzy sets, needed in this book, are also in Chapter 2: (1) in Section 2. 5 we discuss how we have dealt in the past with determining max/min(Z)for Z a fuzzy set representing the value of anobjective function in a fuzzy optimization problem; (2) in Section 2.
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Table of contents (28 chapters)
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Front Matter
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Introduction
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Front Matter
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Applications
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Front Matter
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Unfinished Business
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Front Matter
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Reviews
From the reviews:
"This timely research monograph is a very much needed compendium of recent developments in the methodologies and applications of Monte Carlo fuzzy optimization and fuzzy modeling. ... Overall the writing is lucid and well supported by convincing and highly motivating comments. ... All in all, this is a highly welcome publication which will undoubtedly appeal to the fuzzy set research community." (Witold Pedrycz, Zentralblatt MATH, Vol. 1148, 2008)
Bibliographic Information
Book Title: Monte Carlo Methods in Fuzzy Optimization
Authors: James J. Buckley, Leonard J. Jowers
Series Title: Studies in Fuzziness and Soft Computing
DOI: https://doi.org/10.1007/978-3-540-76290-4
Publisher: Springer Berlin, Heidelberg
eBook Packages: Engineering, Engineering (R0)
Copyright Information: Springer-Verlag Berlin Heidelberg 2008
Hardcover ISBN: 978-3-540-76289-8Published: 20 February 2008
Softcover ISBN: 978-3-642-09516-0Published: 22 November 2010
eBook ISBN: 978-3-540-76290-4Published: 03 December 2007
Series ISSN: 1434-9922
Series E-ISSN: 1860-0808
Edition Number: 1
Number of Pages: XIII, 260
Topics: Artificial Intelligence, Mathematical and Computational Engineering