Studies in Fuzziness and Soft Computing

By: James J. Buckley, Leonard J. Jowers

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Hardcover | 20 February 2008

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276 Pages

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24.13 x 16.51 x 1.91

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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.

Industry Reviews

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"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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Introduction
Introduction	p. 3
Fuzzy Sets	p. 9
Crisp Random Numbers and Vectors	p. 29
Random Fuzzy Numbers and Vectors	p. 35
Tests for Randomness	p. 43
Applications
Fuzzy Monte Carlo Method	p. 57
Fully Fuzzified Linear Programming I	p. 67
Fully Fuzzified Linear Programming II	p. 75
Fuzzy Multiobjective LP	p. 81
Solving Fuzzy Equations	p. 89
Fuzzy Linear Regression I	p. 117
Univariate Fuzzy Nonlinear Regression	p. 127
Multivariate Nonlinear Regression	p. 139
Fuzzy Linear Regression II	p. 155
Fuzzy Two-Person Zero-Sum Games	p. 165
Fuzzy Queuing Models	p. 175
Unfinished Business
Fuzzy Min-Cost Capacitated Network	p. 187
Fuzzy Shortest Path Problem	p. 191
Fuzzy Max-Flow Problem	p. 195
Inventory Control: Known Demand	p. 199
Inventory Control: Fuzzy Demand	p. 205
Inventory Control: Backordering	p. 213
Fuzzy Transportation Problem	p. 217
Fuzzy Integer Programming	p. 223
Fuzzy Dynamic Programming	p. 227
Fuzzy Project Scheduling/PERT	p. 231
Max/Min Fuzzy Function	p. 237
Summary, Conclusions, Future Research
Summary, Conclusions, Future Research	p. 243
Index	p. 247
List of Figures	p. 253
List of Tables	p. 257
Table of Contents provided by Blackwell. All Rights Reserved.

Studies in Fuzziness and Soft Computing

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

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