Monte Carlo Methods in Fuzzy Optimization - Jowers, Leonard J.

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Résumé :
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.

Sommaire:
Part I: Introduction 1 Introduction 3 2 Fuzzy Sets 3 Crisp Random Numbers and Vectors 4 Random Fuzzy Numbers and Vectors 5 Tests for Randomness Part II: Applications 6 Fuzzy Monte Carlo Method 7 Fully Fuzzi?ed Linear Programming I 8 Fully Fuzzi?ed Linear Programming II 9 Fuzzy Multiobjective LP 10 Solving Fuzzy Equations 11 Fuzzy Linear Regression I 12 Univariate Fuzzy Nonlinear Regression 13 Multivariate Nonlinear Regression 14 Fuzzy Linear Regression II 15 Fuzzy Two-Person Zero-Sum Games 16 Fuzzy Queuing Models Part III: Unfinished Business 17 Fuzzy Min-Cost Capacitated Network 18 Fuzzy Shortest Path Problem 19 Fuzzy Max-Flow Problem 20 Inventory Control: Known Demand 21 Inventory Control: Fuzzy Demand 22 Inventory Control: Backordering 23 Fuzzy Transportation Problem 24 Fuzzy Integer Programming 25 Fuzzy Dynamic Programming 26 Fuzzy Project Scheduling/PERT 27 Max/Min Fuzzy Function Part IV: Summary, Conclusions, Future Research 28 Summary, Conclusions, Future Research