An Introduction to Fuzzy Sets

142 Pages·2020·31.084 MB·English

by  Valdemar F. Andersen

MATHEMATICS RESEARCH DEVELOPMENTS

A I
N NTRODUCTION TO
FUZZY SETS

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M R
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D
EVELOPMENTS

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MATHEMATICS RESEARCH DEVELOPMENTS

A I
N NTRODUCTION TO
FUZZY SETS

VALDEMAR F. ANDERSEN
EDITOR
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Library of Congress Cataloging-in-Publication Data

Names: Andersen, Valdemar F., editor. Title: An introduction to fuzzy sets / Valdemar F. Andersen, editor.
Description: New York : Nova Science Publishers, [2020] | Series: Mathematics research developments | Includes bibliographical references and
index. | Summary: "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"-- Provided by publisher.
Identifiers: LCCN 2020020544 (print) | LCCN 2020020545 (ebook) | ISBN 9781536180121 (paperback) | ISBN 9781536180138 (adobe pdf)
Subjects: LCSH: Quality of life--Portugal. | Quality of life. | Fuzzy sets. | Social sciences--Mathematics.
Classification: LCC HN594 .I47 2020 (print) | LCC HN594 (ebook) | DDC 306.09469--dc23
LC record available at https://lccn.loc.gov/2020020544
LC ebook record available at https://lccn.loc.gov/2020020545

Published by Nova Science Publishers, Inc. † New York
CONTENTS

Preface vii
Chapter 1 Quality of Life: Urban versus Rural Analysis
Based on Fuzzy Sets Approach 1
Andreia Dionísio and Conceição Rego
Chapter 2 Economically Speaking, Are Happiness and
HDI the Same? The Fuzzy-Set Approach 33
Andreia Dionísio and Paulo Ferreira
Chapter 3 Implementation of Fuzzy Logic
and Neuro-Fuzzy in Industry 59
Raheleh Jafari, Sina Razvarz,
Alexander Gegov and Saeed Razvarz
Chapter 4 Lotfi Zadeh’s Theory of Fuzzy Sets in Decision-
Making Process for Oil and Gas Production 87
Vidadi Bakhishov and Elmira Isayeva
Chapter 5 Fuzziness-Randomness Modeling of Plasma
Disruption in First Wall of Fusion Reactor
Using Type I Fuzzy Random Set 91
Debabrata Datta and Rashmi Bhardwaj
vi Contents
Chapter 6 Application of a Standard Fuzzy
Arithmetic Method 115
Sangeeta Kumari
Index 125
PREFACE

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.
viii Valdemar F. Andersen
Chapter 1 - This study provides a comparison of the Quality of Life
(QoL) in urban, intermediate and rural NUTS III regions in Portugal. The
main goal is to identify and analyse the necessary and sufficient conditions
for high levels of QoL in those different regions. Those areas are
distinguished based on the population in rural areas (population density),
share of population in rural areas and size of urban centres. The authors use
data provided by several institutions, through Statistics Portugal and
PORDATA. The Gini Index is the proxy used for QoL, i.e., the higher the
Gini Index, the lower the global development and consequently QoL. The
domains of QoL studied are: (i) living material conditions; (ii) productive
activity; (iii) health; (iv) education; (v) leisure and social interactions; (vi)
physical security; (vii) governance; and (viii) natural living conditions. In
order to obtain these domains, the authors use exploratory factor analysis.
Having the domains as conditions, fuzzy sets are applied in order to evaluate
the necessary and sufficient conditions in urban and rural regions. The
authors’ results point to some similar and other different necessary and
sufficient conditions for rural and urban regions; for example, a higher Gini
Index is related to a less ageing population and access to health services,
both in rural and urban regions.
Chapter 2 - The Human Development Index (HDI) has been an indicator
used to evaluate various aspects of human development since the 1990s.
Subject to several criticisms, namely the fact that it does not measure some
kinds of relevant variables, the HDI has undergone several transformations
in its calculation. In parallel, other indices have been used to measure other
situations. For example, the World Happiness Report (WHR) is an annual
publication of the United Nations Sustainable Development Solutions
Network, created to measure a happiness index, whose assumptions are
different. The objective of this research is to identify the necessary and
sufficient conditions for higher HDI levels and to determine whether the
same pattern can be used to explain the happiness index. The questions under
study are: “Is the HDI mostly driven by economic forces? In the end, do
happiness and human development have the same basis? Which are the Life
and Economic necessary and sufficient conditions to reach high levels of
HDI and WHI?”