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Some results of fuzzy BCK-filters

Authors
Journal
Information Sciences
0020-0255
Publisher
Elsevier
Publication Date
Volume
130
Identifiers
DOI: 10.1016/s0020-0255(00)00075-x
Keywords
  • Bck-Algebra
  • (Fuzzy) Bck-Filter
  • Fuzzy Bck-Filter Generated By A Fuzzy Set
  • Distributive Lattice
Disciplines
  • Mathematics

Abstract

Abstract Let X be a bounded BCK-algebra and f a fuzzy set in X. If a fuzzy BCK-filter μ in X satisfies that (i) f⩽ μ, (ii) for any fuzzy BCK-filter ν in X, f⩽ ν implies μ⩽ ν, then μ is said to be generated by f and denote μ by [ f) for short. In the present paper, we give a procedure to construct the [ f) by f. As applications of this result we prove that the set of all fuzzy BCK-filters in a bounded BCK-algebra forms a complete and infinitely distributive lattice.

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