7,366 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
An exact algorithm for linear optimization problem subject to max-product fuzzy relational inequalities with fuzzy constraints
Fuzzy relational inequalities with fuzzy constraints (FRI-FC) are the
generalized form of fuzzy relational inequalities (FRI) in which fuzzy
inequality replaces ordinary inequality in the constraints. Fuzzy constraints
enable us to attain optimal points (called super-optima) that are better
solutions than those resulted from the resolution of the similar problems with
ordinary inequality constraints. This paper considers the linear objective
function optimization with respect to max-product FRI-FC problems. It is proved
that there is a set of optimization problems equivalent to the primal problem.
Based on the algebraic structure of the primal problem and its equivalent
forms, some simplification operations are presented to convert the main problem
into a more simplified one. Finally, by some appropriate mathematical
manipulations, the main problem is transformed into an optimization model whose
constraints are linear. The proposed linearization method not only provides a
super-optimum (that is better solution than ordinary feasible optimal
solutions) but also finds the best super-optimum for the main problem. The
current approach is compared with our previous work and some well-known
heuristic algorithms by applying them to random test problems in different
sizes.Comment: 29 pages, 8 figures, 7 table
Max-min Learning of Approximate Weight Matrices from Fuzzy Data
In this article, we study the approximate solutions set of an
inconsistent system of fuzzy relational equations . Using the norm, we compute by an explicit
analytical formula the Chebyshev distance , where is the set of second members of the
consistent systems defined with the same matrix . We study the set
of Chebyshev approximations of the second member i.e.,
vectors such that , which is
associated to the approximate solutions set in the following sense:
an element of the set is a solution vector of a system where . As main results, we
describe both the structure of the set and that of the set
. We then introduce a paradigm for learning weight
matrices that relates input and output data from training data. The learning
error is expressed in terms of the norm. We compute by an explicit
formula the minimal value of the learning error according to the training data.
We give a method to construct weight matrices whose learning error is minimal,
that we call approximate weight matrices.
Finally, as an application of our results, we show how to learn approximately
the rule parameters of a possibilistic rule-based system according to multiple
training data
Interval linear systems as a necessary step in fuzzy linear systems
International audienceThis article clarifies what it means to solve a system of fuzzy linear equations, relying on the fact that they are a direct extension of interval linear systems of equations, already studied in a specific interval mathematics literature. We highlight four distinct definitions of a systems of linear equations where coefficients are replaced by intervals, each of which based on a generalization of scalar equality to intervals. Each of the four extensions of interval linear systems has a corresponding solution set whose calculation can be carried out by a general unified method based on a relatively new concept of constraint intervals. We also consider the smallest multidimensional intervals containing the solution sets. We propose several extensions of the interval setting to systems of linear equations where coefficients are fuzzy intervals. This unified setting clarifies many of the anomalous or inconsistent published results in various fuzzy interval linear systems studies
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