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Monte Carlo Methods in Fuzzy Optimization

  • Book
  • © 2008

Overview

Authors:
  1. James J. Buckley
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  2. Leonard J. Jowers
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  • 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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Table of contents (28 chapters)

  1. Front Matter

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  2. Introduction

    1. Front Matter

      Pages 1-1
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    2. Introduction

      • James J. Buckley, Leonard J. Jowers
      Pages 3-7

    3. Fuzzy Sets

      • James J. Buckley, Leonard J. Jowers
      Pages 9-28

    4. Crisp Random Numbers and Vectors

      • James J. Buckley, Leonard J. Jowers
      Pages 29-34

    5. Random Fuzzy Numbers and Vectors

      • James J. Buckley, Leonard J. Jowers
      Pages 35-42

    6. Tests for Randomness

      • James J. Buckley, Leonard J. Jowers
      Pages 43-53

  3. Applications

    1. Front Matter

      Pages 55-55
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    2. Fuzzy Monte Carlo Method

      • James J. Buckley, Leonard J. Jowers
      Pages 57-65

    3. Fully Fuzzified Linear Programming I

      • James J. Buckley, Leonard J. Jowers
      Pages 67-73

    4. Fully Fuzzified Linear Programming II

      • James J. Buckley, Leonard J. Jowers
      Pages 75-80

    5. Fuzzy Multiobjective LP

      • James J. Buckley, Leonard J. Jowers
      Pages 81-88

    6. Solving Fuzzy Equations

      • James J. Buckley, Leonard J. Jowers
      Pages 89-115

    7. Fuzzy Linear Regression I

      • James J. Buckley, Leonard J. Jowers
      Pages 117-125

    8. Univariate Fuzzy Nonlinear Regression

      • James J. Buckley, Leonard J. Jowers
      Pages 127-137

    9. Multivariate Nonlinear Regression

      • James J. Buckley, Leonard J. Jowers
      Pages 139-154

    10. Fuzzy Linear Regression II

      • James J. Buckley, Leonard J. Jowers
      Pages 155-164

    11. Fuzzy Two-Person Zero-Sum Games

      • James J. Buckley, Leonard J. Jowers
      Pages 165-173

    12. Fuzzy Queuing Models

      • James J. Buckley, Leonard J. Jowers
      Pages 175-184

  4. Unfinished Business

    1. Front Matter

      Pages 185-185
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Keywords

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.

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

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