An Introduction to Fuzzy Sets

Contents
Preface
Chapter 1
Quality of Life:  Urban versus Rural Analysis  Based on Fuzzy Sets Approach
	Abstract
	Introduction
	Methods
	Results
		Factor Analysis
		Causal Analysis
	Conclusion
	Acknowledgments
	References
	Biographical Sketches
Chapter 2
Economically Speaking,  Are Happiness and HDI the Same?  The Fuzzy-Set Approach
	Abstract
	1. Introduction
	2. Data and Methods
		2.1. The Data
		2.2. Methods
	3. Results
		3.1. Factor Analysis
		Fuzzy Set Analysis
	Conclusion
	References
	Biographical Sketches
Chapter 3
Implementation of Fuzzy Logic  and Neuro-Fuzzy in Industry
	Abstract
	Introduction
	Applications of Fuzzy Logic  in Industrial Engineering
		Mathematical Preliminaries
			Definition 1 (Fuzzy Variable)
			Definition 2 (Fuzzy Number)
			Remark
			Definition 3 (Fuzzy Derivative)
			Fuzzy If-Then Rules
		Background and Related Work
		Fuzzy Expert System
		Advantageous and Drawbacks of Fuzzy Based Systems
		Example of Fuzzy Logic Technique
	Applications of Neuro-Fuzzy  in Industrial Engineering
		Neural Systems
			Biological Neural Network
			Artificial Neural Networks
	Background and Related Work
		Example of Neuro-Fuzzy Technique
	Conclusion
	References
Chapter 4
Lotfi Zadeh’s Theory of Fuzzy  Sets in Decision-Making Process  for Oil and Gas Production
	Annotation
	References
Chapter 5
Fuzziness-Randomness Modeling of Plasma Disruption in First Wall  of Fusion Reactor Using Type I  Fuzzy Random Set
	Abstract
	1. Introduction
	2. The First Wall of Fusion Reactor
		2.1. Physical Structure
		2.2. Mathematical Modeling of Heat Generation in First Wall
		2.3. Melting of Solid Region (First Wall)
		2.4. Evaporation of Solid Region (First Wall)
		2.5. Alpha Cut of a Fuzzy Variable and Fuzzy Random Variable
			2.5.1. Fuzzy Random Variable
				2.5.1.1. Definition
				2.5.1.2. Theorem
				2.5.1.3. Definition
				2.5.1.4. Definition
		2.6. Fuzzy Random Variable Valued Gaussian Function
			2.6.1. Definition
		2.7. Fuzzy Random Variable Valued Gaussian Function
			2.7.1. Lemma
			2.7.2. Definition
			2.7.3. Theorem
			2.7.4. Theorem
			2.7.5. Proof
	3. Uncertainty Modeling
	4. Results and Discussions
	Conclusion
	References
Chapter 6
Application of a Standard  Fuzzy Arithmetic Method
	Abstract
	Introduction
	Methods
		Reservoir Operation Model
	A Standard Fuzzy Arithmetic Method
		Step 1. Decomposition of Fuzzy Numbers
		Step 2. Application of an Interval Arithmetic (Moore 1966)
		Step 3. Recompositions of the Output Intervals
	Fuzzy Ranking Method
	References
	Biographical Sketch
Index
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