One-to-one correspondences between \(\varepsilon\)-partitions, \((1-\varepsilon)\)-equivalences and \(\varepsilon\)-pseudometrics

DOI10.1016/S0165-0114(00)00127-5zbMath1010.03044MaRDI QIDQ1349180

O. Diekmann

Publication date: 21 May 2002

Published in: Fuzzy Sets and Systems (Search for Journal in Brave)

zbMATH Keywords

fuzzy partitionfuzzy equality

Mathematics Subject Classification ID

Theory of fuzzy sets, etc. (03E72)

Related Items (7)

Compatibility of t-norms with the concept of \(\varepsilon\)-partition ⋮ Three-way fuzzy partitions defined by shadowed sets ⋮ Fuzzy \(\delta\)-\(\varepsilon\)-partitions. ⋮ Classification based on L-fuzzy sets1 ⋮ Necessary and sufficient conditions for generalized uniform fuzzy partitions ⋮ Lattice-valued \(F\)-transforms and similarity relations ⋮ \(I\)-fuzzy equivalence relations and \(I\)-fuzzy partitions

Cites Work

• On fuzzy equivalence. I
• Additive fuzzy measures and integrals. I
• Probability of fuzzy events defined as denumerable additivity measure
• Fuzzy partitions and relations; an axiomatic basis for clustering
• Fuzzy partitions with the connectives \(T_ \infty{},S_ \infty\)
• The entropy of fuzzy dynamical systems and generators
• \({\mathcal T}\)-partitions
• q-similitudes and q-fuzzy partitions
• Fuzzy \(\delta\)-\(\varepsilon\)-partitions.
• Similarity relations, fuzzy partitions, and fuzzy orderings
• A new approach to clustering
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