Metric Spaces of Fuzzy Sets: Theory and Applications

The primary aim of the book is to provide a systematic development of the theory of metric spaces of normal, upper semicontinuous fuzzy convex fuzzy sets with compact support sets, mainly on the base space ℜn. An additional aim is to sketch selected applications in which these metric space results and methods are essential for a thorough mathematical analysis. This book is distinctly mathematical in its orientation and style, in contrast with many of the other books now available on fuzzy sets, which, although all making use of mathematical formalism to some extent, are essentially motivated by and oriented towards more immediate applications and related practical issues. The reader is assumed to have some previous undergraduate level acquaintance with metric spaces and elementary functional analysis. Contents:Fuzzy SetsSpaces of Subsets of ℜnCompact Convex Subsets of ℜnSet Valued MappingsCrisp GeneralizationsThe Space εnMetrics on εnCompactness CriteriaGeneralizationsFuzzy Set Valued Mappings of Real VariablesFuzzy Random VariablesComputational MethodsFuzzy Differential EquationsOptimization Under UncertaintyFuzzy Iterations and Image Processing Readership: Mathematicians and computer scientists. keywords:Metric Spaces;Multifunctions;Fuzzy Sets;Fuzzy Data Fitting;Fuzzy Dynamical Systems;Iterated Fuzzy Systems “… is a valuable addition to the literature about fuzzy analysis, leading the reader to the edge of current research.” Mathematical Reviews “… the book seems to be the only, and thus valuable, source of mathematical concepts and results on fuzzy sets and functions, which are presented in a clear, and quite rigorous, format.” Journal of Classification