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The book is a benefit for graduate and postgraduate students in the
areas of operations research, decision theory, optimization theory,
linear algebra, interval analysis and fuzzy sets. The book will
also be useful for the researchers in the respective areas. The
first part of the book deals with decision making problems and
procedures that have been established to combine opinions about
alternatives related to different points of view. Procedures based
on pairwise comparisons are thoroughly investigated. In the second
part we investigate optimization problems where objective functions
and constraints are characterized by extremal operators such as
maximum, minimum or various triangular norms (t-norms). Matrices in
max-min algebra are useful in applications such as automata theory,
design of switching circuits, logic of binary relations, medical
diagnosis, Markov chains, social choice, models of organizations,
information systems, political systemsand clustering. The input
data in real problems are usually not exact and can be
characterized by interval values."
Linear programming attracted the interest of mathematicians
during and after World War II when the first computers were
constructed and methods for solving large linear programming
problems were sought in connection with specific practical problems
for example, providing logistical support for the U.S. Armed Forces
or modeling national economies. Early attempts to apply linear
programming methods to solve practical problems failed to satisfy
expectations. There were various reasons for the failure. One of
them, which is the central topic of this book, was the inexactness
of the data used to create the models. This phenomenon, inherent in
most pratical problems, has been dealt with in several ways. At
first, linear programming models used "average" values of
inherently vague coefficients, but the optimal solutions of these
models were not always optimal for the original problem itself.
Later researchers developed the stochastic linear programming
approach, but this too has its limitations. Recently, interest has
been given to linear programming problems with data given as
intervals, convex sets and/or fuzzy sets. The individual results of
these studies have been promising, but the literature has not
presented a unified theory. Linear Optimization Problems with
Inexact Data attempts to present a comprehensive treatment of
linear optimization with inexact data, summarizing existing results
and presenting new ones within a unifying framework."
Linear programming attracted the interest of mathematicians during
and after World War II when the first computers were constructed
and methods for solving large linear programming problems were
sought in connection with specific practical problems for example,
providing logistical support for the U.S. Armed Forces or modeling
national economies. Early attempts to apply linear programming
methods to solve practical problems failed to satisfy expectations.
There were various reasons for the failure. One of them, which is
the central topic of this book, was the inexactness of the data
used to create the models. This phenomenon, inherent in most
practical problems, has been dealt with in several ways. At first,
linear programming models used average values of inherently vague
coefficients, but the optimal solutions of these models were not
always optimal for the original problem itself. Later researchers
developed the stochastic linear programming approach, but this too
has its limitations. Recently, interest has been given to linear
programming problems with data given as intervals, convex sets
and/or fuzzy sets. literature has not presented a unified theory.
Linear Optimization Problems with Inexact Data attempts to present
a comprehensive treatment of linear optimization with inexact data,
summarizing existing results and presenting new ones within a
unifying framework.
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