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Congruence classes of fuzzy sets form a Banach space

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Publication:1192762
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DOI10.1016/0022-247X(91)90182-YzbMath0769.46057MaRDI QIDQ1192762

Phil Diamond

Publication date: 27 September 1992

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)


zbMATH Keywords

metricasymmetry classes of normal, fuzzy convex fuzzy setslinear structure of the space of fuzzy setsset of asymmetry classes


Mathematics Subject Classification ID

Fuzzy functional analysis (46S40)


Related Items

Possibilities as cumulative subjective probabilities and a norm on the space of congruence classes of fuzzy numbers motivated by an expected utility functional, Applying the concept of null set to solve the fuzzy optimization problems



Cites Work

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  • The concept of normality for fuzzy random variables
  • \(L_p\) metrics for compact convex sets
  • Fuzzy real numbers as Dedekind cuts with respect to a multiple-valued logic
  • Characterization of compact subsets of fuzzy sets
  • Normed vector spaces consisting of classes of convex sets
  • A pre-Hilbert space consisting of classes of convex sets
  • Limit theorems for fuzzy random variables
  • A Uniqueness Theorem for the Steiner Point of a Convex Region
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