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Invariant probabilistic metrizability of fuzzy neighbourhood groups

Authors
Journal
Fuzzy Sets and Systems
0165-0114
Publisher
Elsevier
Publication Date
Volume
47
Issue
2
Identifiers
DOI: 10.1016/0165-0114(92)90182-4
Keywords
  • Fuzzy Neighbourhood Space
  • Fuzzy Uniform Space
  • Fuzzy Neighbourhood Group
  • N-Local Compactness
  • N-Open Function
  • Fuzzy Real Numbers
  • Fuzzy (Probabilistic) Metric
  • Fuzzy Absolute Value Function
  • Fuzzy Metric Neighbourhood Space
  • α-Level Space
  • Wnt2-Space
Disciplines
  • Mathematics

Abstract

Abstract We introduce the notions of N-local compactness and N-openess in fuzzy neighbourhood spaces and in fuzzy neighbourhood groups, together with some characterizations for them. In particular, we prove that a fuzzy neighbourhood space is N-locally compact if and only if its α-level spaces, for all 0< α<1, are locally compact. A similar criterion is established for N-open functions. We also introduce the notion of fuzzy absolute value functions on groups. We show that there exists a 1-1 correspondence between invariant fuzzy (probabilistic) pseudo-metrics on groups and fuzzy absolute value functions. We establish theorems on fuzzy (probabilistic) pseudo-metrizability of fuzzy neighbourhood groups. Finally, fuzzy (probabilistic) metrizability of quotient fuzzy neighbourhood groups is also taken into account.

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