An Introduction to Fuzzy Sets

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Valdemar F. Andersen (Editor)

Series: Mathematics Research Developments
BISAC: MAT018000

An Introduction to Fuzzy Sets provides a comparison of the quality of life in urban, intermediate and rural NUTS III regions in Portugal, with the main goal of identifying and analysing the necessary and conditions for a high quality of life in those different regions.
The authors assess the necessary and sufficient conditions for higher Human Development Index levels, aiming to determine whether the same pattern could be used to explain the happiness index.
In order to represent the applications of fuzzy set theory as well as neuro-fuzzy in industry, a literature review of these topics is carried out. As some researchers have efficiently utilized fuzzy logic and neuro-fuzzy, in-depth discussions are provided for stimulating future investigations.
Following this, using the L. Zadeh theory of fuzzy sets, the authors consider all types of uncertainties in oil fields and oil production to make a decision as to what model is best in such a fuzzy environment.
Additionally, several challenges are explored, such as: the fuzzy random finite difference numerical method, possibilistic uncertainty modeling, and the development of a fuzzy Wilks’ theorem to model the hybrid structure of randomness and fuzziness modeling.
In closing, a standard fuzzy arithmetic method is used for solving fuzzy equations, as well as for the optimization of fuzzy objectives. The fuzzy variable of the equation is fuzzified using a fuzzy set. (Imprint: Nova)

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Tadle of Contents

Preface

Chapter 1. Quality of Life: Urban versus Rural Analysis Based on Fuzzy Sets Approach
(Andreia Dionísio and Conceição Rego, Cefage, Department of Management, Universidade de Évora, Évora, Portugal, and others)

Chapter 2. Economically Speaking, Are Happiness and HDI the Same? The Fuzzy-Set Approach
(Andreia Dionísio and Paulo Ferreira, Cefage, Department of Management, Universidade de Évora, Évora, Portugal, and others)

Chapter 3. Implementation of Fuzzy Logic and Neuro-Fuzzy in Industry
(Raheleh Jafari, Sina Razvarz, Alexander Gegov and Saeed Razvarz, School of Design, University of Leeds, Leeds, UK, and others)

Chapter 4. Lotfi Zadeh’s Theory of Fuzzy Sets in Decision-Making Process for Oil and Gas Production
(Vidadi Bakhishov and Elmira Isayeva, Agency of Small Business Development, Ministry of Economics of Azerbaijan Republic, Baku, Azerbaijan,

Chapter 5. Fuzziness-Randomness Modeling of Plasma Disruption in First Wall of Fusion Reactor Using Type I Fuzzy Random Set
(Debabrata Datta and Rashmi Bhardwa, Senior Scientist-H, Head, Radiological Physics and Advisory Division, Bhabha Atomic Research Centre, Anushaktinagar, Mumbai, India, and others)

Chapter 6. Application of a Standard Fuzzy Arithmetic Method
(Sangeeta Kumari, PhD, Department of Civil Engineering, NIT Jamshedpur, Jharkhand, India)

Index

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