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Generalized Concavity in Fuzzy Optimization and Decision Analysis (Hardcover, 2002 ed.)
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Generalized Concavity in Fuzzy Optimization and Decision Analysis (Hardcover, 2002 ed.)
Series: International Series in Operations Research & Management Science, 41
Expected to ship within 10 - 15 working days
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Convexity of sets in linear spaces, and concavity and convexity of
functions, lie at the root of beautiful theoretical results that
are at the same time extremely useful in the analysis and solution
of optimization problems, including problems of either single
objective or multiple objectives. Not all of these results rely
necessarily on convexity and concavity; some of the results can
guarantee that each local optimum is also a global optimum, giving
these methods broader application to a wider class of problems.
Hence, the focus of the first part of the book is concerned with
several types of generalized convex sets and generalized concave
functions. In addition to their applicability to nonconvex
optimization, these convex sets and generalized concave functions
are used in the book's second part, where decision-making and
optimization problems under uncertainty are investigated.
Uncertainty in the problem data often cannot be avoided when
dealing with practical problems. Errors occur in real-world data
for a host of reasons. However, over the last thirty years, the
fuzzy set approach has proved to be useful in these situations. It
is this approach to optimization under uncertainty that is
extensively used and studied in the second part of this book.
Typically, the membership functions of fuzzy sets involved in such
problems are neither concave nor convex. They are, however, often
quasiconcave or concave in some generalized sense. This opens
possibilities for application of results on generalized concavity
to fuzzy optimization. Despite this obvious relation, applying the
interface of these two areas has been limited to date. It is hoped
that the combination of ideas and results from the field of
generalized concavity on the one hand and fuzzy optimization on the
other hand outlined and discussed in Generalized Concavity in Fuzzy
Optimization and Decision Analysis will be of interest to both
communities. Our aim is to broaden the classes of problems that the
combination of these two areas can satisfactorily address and
solve.
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