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Some complete metrics on spaces of fuzzy subsets

Authors
Journal
Fuzzy Sets and Systems
0165-0114
Publisher
Elsevier
Publication Date
Volume
130
Issue
3
Identifiers
DOI: 10.1016/s0165-0114(02)00120-3
Keywords
  • Lp
  • ∞-Metrics
  • Lp-Metrics
  • Completion Of Thelp
  • ∞-Metrics
  • Completion Of Thelp-Metrics
Disciplines
  • Mathematics

Abstract

Abstract The classes of the L p,∞ - and L p -metrics play an important role to develop a probability theory in fuzzy sample spaces. All of these metrics are known to be separable, but not complete. The classes are closely related as for each L p,∞ -metric there exists some L p -metric which induces the same topology. This paper deals with the completion of the L p,∞ - and L p -metrics. We can also show that the relationship between the classes of L p,∞ - and L p -metrics still holds for the obtained respective classes of their completions.

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