Advisory Committee Chair
James J Buckley
Advisory Committee Members
Ian Knowles
Kevin D Reilly
Peter Slarter
Wei-Shen Hsia
Document Type
Dissertation
Date of Award
2007
Degree Name by School
Doctor of Philosophy (PhD) College of Arts and Sciences
Abstract
This thesis is devoted to solve fuzzy optimization problems using Monte Carlo methods. In the ¯rst four chapters, we are ¯nding a fuzzy function that best ex- plains the fuzzy data. We study di®erent models; linear, polynomial, exponential and logarithmic. To ¯nd the best model that explains some data, we look for the one that minimizes some error measure. We use several popular error measures. Also, we discuss and compare our results with previous published results. Then we study a fuzzy optimization problem in queuing theory where it is used to model a web site. The variables are a mix of crisp variables -to express the system capacity and the number of servers- and fuzzy variables- to express the arrival rate and service rate of any server-. The objective is to maximize the fuzzy pro¯t function. This problem has no known algorithmic solution; and previous results have investigated only 16 cases. The last problem is a two-person zero-sum game with fuzzy payo®s and fuzzy mixed strategy. We, ¯rst, de¯ne the fuzzy values (V I ; V II) and an optimal fuzzy mixed strategy for the players. Then, we use our Monte Carlo Method to investigate the conjecture V I = V II .
Recommended Citation
Abdalla, Areeg, "Monte Carlo Studies With Random Fuzzy Numbers" (2007). All ETDs from UAB. 3658.
https://digitalcommons.library.uab.edu/etd-collection/3658