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Irreducibility in algebraic fuzzy systems

Authors
Journal
Fuzzy Sets and Systems
0165-0114
Publisher
Elsevier
Publication Date
Volume
41
Issue
2
Identifiers
DOI: 10.1016/0165-0114(91)90227-h
Keywords
  • Algebraic Closure Set System
  • Fuzzyl-Subset
  • Inclusion Binary Operation
  • Prime Fuzzyl-Subset
  • Hull-Kernel Topology
  • Maximal Fuzzyl-Subset
  • Irreducible Element
Disciplines
  • Mathematics

Abstract

Abstract Inclusion invariant binary operations, on an algebraic closure set system L , are extended to a fuzzy L -system. The notions of prime (maximal) fuzzy L -subset of a nonepty set X having truth values in a complete Browerian lattice L are introduced and are completely determined in terms of pairs ( P, α), where P is a prime (maximal) element of L and α is an irreducible element (dual-atom) of L. It is observed that the space of all prime fuzzy L -subsets of X, together with its hull-kernel topology, is homeomorphic to the product of the spaces of prime elements of L and of irreducible elements of L, equipped with hull-kernel topologies. Also distributivity and irreducible elements of the fuzzy L -system on X are discussed.

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