Metric Spaces of Fuzzy Sets: Theory and ApplicationsThe 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 ?n. 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
Preface | 1 |
Metrics on | 7 |
Set Valued Mappings | 23 |
Crisp Generalizations | 108 |
Computational Methods | 115 |
Fuzzy Differential Equations | 129 |
The Space | 131 |
CONTENTS ix | 137 |
Fuzzy Iterations and Image Processing | 143 |
Appendix on Metric Spaces | 155 |
Bibliography | 161 |
Symbols and Abbreviations | 171 |
Other editions - View all
Metric Spaces of Fuzzy Sets: Theory and Applications Phil Diamond,Peter Kloeden Limited preview - 1994 |
Common terms and phrases
Aumann integrable Banach space Bibliographical Notes Blaschke Blasi differentiable Bobylev Cauchy sequence closed subset compact convex subsets compact subset complete metric space cone convex sets D₁ defined definition denote diam doo metric dp(u equileftcontinuous equivalent Example Ɛ¹ F(to follows Fréchet differential fuzzy convex fuzzy differential equation fuzzy random variables fuzzy set valued fuzzy star shaped Hausdorff distance Hausdorff metric Hence Hukuhara derivative Hukuhara difference Hukuhara differentiable inequality integrably bounded Lebesgue measure Lemma Let F level set mappings levelsetwise linear Lipschitz continuous lower semicontinuous Moreover nondecreasing sequence nonempty compact convex nonempty compact subset nonempty subset norm p-Blaschke properties Proposition 6.1.7 Proposition 7.4.9 Puri and Ralescu random variables satisfies selector send uk set valued mapping star shaped sets Steiner centroid support function supremum Theorem topology triangular fuzzy numbers uniformly support-bounded unique upper semicontinuous valued mapping F
Popular passages
Page 163 - P. Diamond and P. Kloeden, Metric spaces of fuzzy sets, Fuzzy Sets and Systems 35 (1990) 241-249.