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In the world of mathematics, the study of fuzzy relations and its
theories are well-documented and a staple in the area of
calculative methods. What many researchers and scientists overlook
is how fuzzy theory can be applied to industries outside of
arithmetic. The framework of fuzzy logic is much broader than
professionals realize. There is a lack of research on the full
potential this theoretical model can reach. Emerging Applications
of Fuzzy Algebraic Structures provides emerging research exploring
the theoretical and practical aspects of fuzzy set theory and its
real-life applications within the fields of engineering and
science. Featuring coverage on a broad range of topics such as
complex systems, topological spaces, and linear transformations,
this book is ideally designed for academicians, professionals, and
students seeking current research on innovations in fuzzy logic in
algebra and other matrices.
In the world of mathematics and computer science, technological
advancements are constantly being researched and applied to ongoing
issues. Setbacks in social networking, engineering, and automation
are themes that affect everyday life, and researchers have been
looking for new techniques in which to solve these challenges.
Graph theory is a widely studied topic that is now being applied to
real-life problems. Advanced Applications of Graph Theory in Modern
Society is an essential reference source that discusses recent
developments on graph theory, as well as its representation in
social networks, artificial neural networks, and many complex
networks. The book aims to study results that are useful in the
fields of robotics and machine learning and will examine different
engineering issues that are closely related to fuzzy graph theory.
Featuring research on topics such as artificial neural systems and
robotics, this book is ideally designed for mathematicians,
research scholars, practitioners, professionals, engineers, and
students seeking an innovative overview of graphic theory.
After developing fuzzy set theory, many contributors focused their
research on the extension of fuzzy sets and their computational
methodologies, strengthening modern science and technology. In some
real-life phenomena, the conventional methods and traditional fuzzy
sets cannot be explained, whereas the extension of fuzzy sets and
effective new computing methods can explain it adequately. This
edited book presents a new view of fuzzy set-measurement methods
entitled "Fuzzy Optimization, Decision Making and Operations
Research: Theory and Applications", which deals with different
perspectives and areas of research. All chapters are divided into
three parts: fuzzy optimization, fuzzy decision-making, and fuzzy
operation research. The goal of this book is to provide a relevant
methodological framework covering the core fields of fuzzy
decision-making method, fuzzy optimization method, fuzzy graphics
method, fuzzy operations research, fuzzy optimization using graph
theory, fuzzy support systems and its real and industrial
applications. For many people, fuzzy words' industrial engineering
and scientific meanings are still an advanced system for improving
modern science and technology. Although fuzzy logic can be applied
to many different areas, people do not know how different fuzzy
approaches can be applied to various products currently on the
market. It is written for professionals who wish to share their
expertise, improve their findings, and provide relevant information
in the fields of fuzzy methods and their application in
decision-making, optimization theory, graph theory and operations
research. This book is aimed at experts and practitioners in the
fields of fuzzy optimization, fuzzy decision-making, and fuzzy
operation research.
This book provides an extensive set of tools for applying fuzzy
mathematics and graph theory to real-life problems. Balancing the
basics and latest developments in fuzzy graph theory, this book
starts with existing fundamental theories such as connectivity,
isomorphism, products of fuzzy graphs, and different types of paths
and arcs in fuzzy graphs to focus on advanced concepts such as
planarity in fuzzy graphs, fuzzy competition graphs, fuzzy
threshold graphs, fuzzy tolerance graphs, fuzzy trees, coloring in
fuzzy graphs, bipolar fuzzy graphs, intuitionistic fuzzy graphs,
m-polar fuzzy graphs, applications of fuzzy graphs, and more. Each
chapter includes a number of key representative applications of the
discussed concept. An authoritative, self-contained, and inspiring
read on the theory and modern applications of fuzzy graphs, this
book is of value to advanced undergraduate and graduate students of
mathematics, engineering, and computer science, as well as
researchers interested in new developments in fuzzy logic and
applied mathematics.
Picture Fuzzy Logic and Its Applications in Decision Making
Problems provides methodological frameworks and the latest
empirical research findings in the field of picture fuzzy
operators, and their applications in scientific research and
real-world engineering problems. Although fuzzy logic can be
applied in a number of different areas, many researchers and
developers are not yet familiar with how picture fuzzy operators
can be applied to a variety of advanced decision-making problems.
Picture fuzzy set is a more powerful tool than fuzzy set or
intuitionistic fuzzy set to tackle uncertainty in a variety
real-world modeling applications. Picture fuzzy set is actually the
generalization of intuitionistic fuzzy set, and intuitionistic
fuzzy set is the generalization of fuzzy set. In this book, the
picture fuzzy sets are investigated, and different types of
operators are defined to solve a number of important decision
making and optimization problems. The hybrid operator on picture
fuzzy set based on the combination of picture fuzzy weighted
averaging operators and picture fuzzy weighted geometric operators
is developed and named Hybrid Picture Fuzzy Weighted Averaging
Geometric (H-PFWAG) operator. Another operator is developed for
interval-valued picture fuzzy environment, which is named Hybrid
Interval-Valued Picture Fuzzy Weighted Averaging Geometric
(H-IVPFWAG) operator. These two operators are then demonstrated as
solutions to Multiple-Attribute Decision-Making (MADM) problems.
The picture fuzzy soft weighted aggregation operators (averaging
and geometric) are defined, and these are applied to develop a
multi-criteria group decision making system. The Dombi operator in
the picture fuzzy environment is then defined and applied to solve
MADM problems. Based on the Dombi operator, several other operators
are defined. These are the picture fuzzy Dombi aggregation
operators, including picture fuzzy Dombi weighted averaging
operator, picture fuzzy Dombi order weighted averaging operator,
picture fuzzy Dombi hybrid averaging operator, picture fuzzy Dombi
weighted geometric operator, picture fuzzy Dombi order weighted
geometric operator, and picture fuzzy Dombi hybrid geometric
operator. Each of these operators are used to solve MADM problems.
An extension picture fuzzy set known as m-polar picture fuzzy set
is proposed and investigated along with many properties of m-polar
picture fuzzy Dombi weighted averaging and geometric operators;
each of these operators are applied to MADM problems. Another
extension of the picture fuzzy set is the interval-valued picture
fuzzy uncertain linguistic environment. In this set,
interval-valued picture fuzzy uncertain linguistic weighted
averaging and geometric operators are developed, and
interval-valued picture fuzzy uncertain linguistic Dombi weighted
aggregation operators are utilized in the MADM process. In the
complex picture fuzzy environment, the authors demonstrate some
complex picture fuzzy weighted aggregation operators to be used in
solving MADM problems. Another approach called MABAC with picture
fuzzy numbers is studied and developed as a multi-attribute group
decision making model. Furthermore, the picture fuzzy linear
programming problem (PFLPP) is initiated, in which the parameters
are picture fuzzy numbers (PFNs). The picture fuzzy optimization
method is applied for solving the PFLPP. This concept is used to
solve the picture fuzzy multi-objective programming problem
(PFMOLPP) under the picture fuzzy environment.
This book provides an extensive set of tools for applying fuzzy
mathematics and graph theory to real-life problems. Balancing the
basics and latest developments in fuzzy graph theory, this book
starts with existing fundamental theories such as connectivity,
isomorphism, products of fuzzy graphs, and different types of paths
and arcs in fuzzy graphs to focus on advanced concepts such as
planarity in fuzzy graphs, fuzzy competition graphs, fuzzy
threshold graphs, fuzzy tolerance graphs, fuzzy trees, coloring in
fuzzy graphs, bipolar fuzzy graphs, intuitionistic fuzzy graphs,
m-polar fuzzy graphs, applications of fuzzy graphs, and more. Each
chapter includes a number of key representative applications of the
discussed concept. An authoritative, self-contained, and inspiring
read on the theory and modern applications of fuzzy graphs, this
book is of value to advanced undergraduate and graduate students of
mathematics, engineering, and computer science, as well as
researchers interested in new developments in fuzzy logic and
applied mathematics.
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