Monte Carlo Methods in Fuzzy Optimization

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,outlinesourun?nishedbusinesswhich 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.

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

Klappentext

This book is a concise and readable introduction to Monte Carlo methods to find good approximate solutions to fuzzy optimization problems. Various basic applications and illustrative examples are presented in an understandable way. The aim of the book is to convince the reader that Monte Carlo methods can be useful in generating approximate solutions to fuzzy optimization problems.

Inhalt
Fuzzy Sets.- Crisp Random Numbers and Vectors.- Random Fuzzy Numbers and Vectors.- Tests for Randomness.- Applications.- Fuzzy Monte Carlo Method.- Fully Fuzzified Linear Programming I.- Fully Fuzzified Linear Programming II.- Fuzzy Multiobjective LP.- Solving Fuzzy Equations.- Fuzzy Linear Regression I.- Univariate Fuzzy Nonlinear Regression.- Multivariate Nonlinear Regression.- Fuzzy Linear Regression II.- Fuzzy Two-Person Zero-Sum Games.- Fuzzy Queuing Models.- Unfinished Business.- Fuzzy Min-Cost Capacitated Network.- Fuzzy Shortest Path Problem.- Fuzzy Max-Flow Problem.- Inventory Control: Known Demand.- Inventory Control: Fuzzy Demand.- Inventory Control: Backordering.- Fuzzy Transportation Problem.- Fuzzy Integer Programming.- Fuzzy Dynamic Programming.- Fuzzy Project Scheduling/PERT.- Max/Min Fuzzy Function.- Summary, Conclusions, Future Research.- Summary, Conclusions, Future Research.