الفهرس 
CHAPTER (1) Basic Concepts of Optimization ProblemOnly 14 pages are availabe for public view
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Abstract
This thesis studies the optimization problems, in particular the problems of linear programming [2], goal programming [7], and game theory [15] and the methods of solving them using fuzzy numbers [29] and neutrosophic numbers [51] to deal with ambiguous and inaccurate information.
The thesis consists of six chapters:
Chapter One: Basic Concepts of Optimization Problems
This chapter is an introduction to the following chapters, as it contains some basic concepts of optimization problems.
The chapter introduces the concept of linear programming, its history, and some of the applications that linear programming contributes to. The chapter also presents some methods for solving linear programming problems. Finally, it introduces some basic concepts of goal programming, game theory, and their applications.
Chapter Two: Fuzzy Linear Programming
This chapter aims to study some basic concepts of fuzzy numbers, intuitionistic fuzzy numbers [37] and generalized fuzzy numbers [40], and how to use them to solve linear programming problems. It also reviews the various arithmetic operations in the case of using fuzzy, intuitionistic fuzzy and generalized numbers. It presents the rank function [40] and how to use it in converting fuzzy numbers into real numbers. It also introduces two novel algorithms used to solve linear programming problems using fuzzy numbers which are:
A Novel Fuzzy Artificial Variable-Free Simplex Algorithm (FAVFSA)
A Novel Dual Fuzzy Artificial Variable-Free Simplex Algorithm (FDAVFSA)
It also reviews a novel hybrid algorithm for solving linear programming problems using generalized fuzzy numbers (generalized fuzzy artificial variable-free cosine simplex algorithm). We use numerical examples to compare the proposed algorithm with the traditional two-phase algorithm in solving fuzzy linear programming problems.
Chapter Three: Neutrosophic Linear Programming
This chapter aims to study some of the basic concepts of neutrosophic numbers [40] and neutrosophic sets [51] and how to use them to solve linear programming problems. It also reviews the various arithmetic operations in the case of using neutrosophic numbers and presents the Rank Function and how to use it in converting fuzzy numbers to neutrosophic numbers. It introduces some new algorithms used to solve linear programming problems using neutrosophic numbers which are:
A Novel Neutrosophic Artificial Variable-Free Simplex Algorithm (NAVFSA)
A Novel Dual Neutrosophic Artificial Variable-Free Simplex Algorithm (NDAVFSA)
We use numerical examples to compare the proposed algorithm with the traditional two-phase algorithm in solving neutrosophic linear programming problems. We also use numerical examples to compare the fuzzy approach with the neutrosophic approach.
Chapter Four: A Multi-Criteria Model for Sustainable Development Goals Using Neutrosophic Goal Programming-Application for Egypt
In this chapter, we present novel fuzzy and neutrosophic goal programming models that incorporate optimal resource allocation to simultaneously satisfy prospective goals on economic development, energy consumption, workforce, and greenhouse gases emission reduction by 2030, applying to Egypt’s key economic sectors. We also compare the outcomes of fuzzy goal programming and neutrosophic goal programming.
The presented models examine opportunities for improvement and the effort required to implement sustainable development plans. We also introduce numerical examples to validate and apply the proposed models.
Chapter Five: A Survey of Game Theory with Neutrosophic Application
In this chapter, we provide a comprehensive background on game theory [73]. Then we present some works linking game theory with neutrosophic sets. The last part of the chapter deals with analyzing work using two major scientific databases (Web of Science and Scopus) by topic, country, year,… etc.
Chapter Six: An Overview of the Bi-Length Memory Effect in the Strictly Alternating Iterated Prisoners Dilemma Game [75]
In this chapter, we study the changing memory in a strictly alternating iterated prisoner dilemma game, which means that the new decision will be made using the pre-previous unit rather than the most recent one. Only the sixteen employed strategies will be specified using finite two-state automata. The computation of strategy payoff will consider implementation mistakes. The dominant strategy will be chosen based on the interaction payoff between each pair of strategies. The Equilibrium points between any heteroclinic three-cycles will be calculated because there is no single strategy that is absolutely dominating. For the space of strategies, S_2 exhibits impressive stable performance unmatched by other strategies.