6,639 research outputs found
Super Fuzzy Matrices and Super Fuzzy Models for Social Scientists
This book introduces the concept of fuzzy super matrices and operations on
them. This book will be highly useful to social scientists who wish to work
with multi-expert models. Super fuzzy models using Fuzzy Cognitive Maps, Fuzzy
Relational Maps, Bidirectional Associative Memories and Fuzzy Associative
Memories are defined here. The authors introduce 13 multi-expert models using
the notion of fuzzy supermatrices. These models are described with illustrative
examples. This book has three chapters. In the first chaper, the basic concepts
about super matrices and fuzzy super matrices are recalled. Chapter two
introduces the notion of fuzzy super matrices adn their properties. The final
chapter introduces many super fuzzy multi expert models.Comment: 280 page
A Divide-and-Conquer Approach for Solving Fuzzy Max-Archimedean t
A system of fuzzy relational equations with the max-Archimedean t-norm composition was considered. The relevant literature indicated that this problem can be reduced to the problem of finding all the irredundant coverings of a binary matrix. A divide-and-conquer approach is proposed to solve this problem and, subsequently, to solve the original problem. This approach was used to analyze the binary matrix and then decompose the matrix into several submatrices such that the irredundant coverings of the original matrix could be constructed using the irredundant coverings of each of these submatrices. This step was performed recursively for each of these submatrices to obtain the irredundant coverings. Finally, once all the irredundant coverings of the original matrix were found, they were easily converted into the minimal solutions of the fuzzy relational equations. Experiments on binary matrices, with the number of irredundant coverings ranging from 24 to 9680, were also performed. The results indicated that, for test matrices that could initially be partitioned into more than one submatrix, this approach reduced the execution time by more than three orders of magnitude. For the other test matrices, this approach was still useful because certain submatrices could be partitioned into more than one submatrix
Fuzzy Interval Matrices, Neutrosophic Interval Matrices and their Applications
The new concept of fuzzy interval matrices has been introduced in this book
for the first time.
The authors have not only introduced the notion of fuzzy interval matrices,
interval neutrosophic matrices and fuzzy neutrosophic interval matrices but
have also demonstrated some of its applications when the data under study is an
unsupervised one and when several experts analyze the problem. Further, the
authors have introduced in this book multiexpert models using these three new
types of interval matrices. The new multi expert models dealt in this book are
FCIMs, FRIMs, FCInMs, FRInMs, IBAMs, IBBAMs, nIBAMs, FAIMs, FAnIMS, etc.
Illustrative examples are given so that the reader can follow these concepts
easily. This book has three chapters. The first chapter is introductory in
nature and makes the book a self-contained one. Chapter two introduces the
concept of fuzzy interval matrices. Also the notion of fuzzy interval matrices,
neutrosophic interval matrices and fuzzy neutrosophic interval matrices, can
find applications to Markov chains and Leontief economic models. Chapter three
gives the application of fuzzy interval matrices and neutrosophic interval
matrices to real-world problems by constructing the models already mentioned.
Further these models are mainly useful when the data is an unsupervised one and
when one needs a multi-expert model. The new concept of fuzzy interval matrices
and neutrosophic interval matrices will find their applications in engineering,
medical, industrial, social and psychological problems. We have given a long
list of references to help the interested reader.Comment: 304 page
Optimizing an Organized Modularity Measure for Topographic Graph Clustering: a Deterministic Annealing Approach
This paper proposes an organized generalization of Newman and Girvan's
modularity measure for graph clustering. Optimized via a deterministic
annealing scheme, this measure produces topologically ordered graph clusterings
that lead to faithful and readable graph representations based on clustering
induced graphs. Topographic graph clustering provides an alternative to more
classical solutions in which a standard graph clustering method is applied to
build a simpler graph that is then represented with a graph layout algorithm. A
comparative study on four real world graphs ranging from 34 to 1 133 vertices
shows the interest of the proposed approach with respect to classical solutions
and to self-organizing maps for graphs
How Many Dissimilarity/Kernel Self Organizing Map Variants Do We Need?
In numerous applicative contexts, data are too rich and too complex to be
represented by numerical vectors. A general approach to extend machine learning
and data mining techniques to such data is to really on a dissimilarity or on a
kernel that measures how different or similar two objects are. This approach
has been used to define several variants of the Self Organizing Map (SOM). This
paper reviews those variants in using a common set of notations in order to
outline differences and similarities between them. It discusses the advantages
and drawbacks of the variants, as well as the actual relevance of the
dissimilarity/kernel SOM for practical applications
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