Monte Carlo Methods in Fuzzy Optimization

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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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.

• Fuzzy
• Fuzzy Statistics
• Mont Carlo Studies
• Random Fuzzy Numbers
• Regression
• fuzzy set
• fuzzy sets
• game theory
• linear optimization
• linear regression
• optimization
• programming

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)

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