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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 Sets
- Spaces of Subsets of ℜn
- Compact Convex Subsets of ℜn
- Set Valued Mappings
- Crisp Generalizations
- The Space εn
- Metrics on εn
- Compactness Criteria
- Generalizations
- Fuzzy Set Valued Mappings of Real Variables
- Fuzzy Random Variables
- Computational Methods
- Fuzzy Differential Equations
- Optimization Under Uncertainty
- Fuzzy Iterations and Image Processing
Readership: Mathematicians and computer scientists.
