JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2018, Vol. 53 ›› Issue (2): 52-64.doi: 10.6040/j.issn.1671-9352.0.2017.403

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Falling fuzzy filters on residuated lattices

PENG Jia-yin   

  1. School of Mathematics and Information Science, Neijiang Normal University, Neijiang 641199, Sichuan, China
  • Received:2017-08-15 Online:2018-02-20 Published:2018-01-31

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Abstract: Using the theory of falling shadows, the fuzzy filter theory of residuated lattices is reestablished. The concepts of falling fuzzy filters, falling fuzzy implicative filters, falling fuzzy Boolean filters, falling fuzzy positive implicative filters and falling fuzzy G-filters on residuated lattices are introduced and their properties are investigated. The relations among them are discussed, and some equivalent characterizations of these filters are obtained. Conditions for a falling shadow to be a falling fuzzy filter, and for a falling fuzzy filter to be a falling fuzzy(positive)implicative filter are given. The relations between a falling fuzzy(implicative, positive implicative, Boolean, G-)filter and fuzzy(implicative, positive implicative, Boolean, G-)filter are studied. It is proved that falling fuzzy(G-)Boolean filter is equivalent to falling fuzzy(positive)implicative filter under certain conditions.

Key words: falling fuzzy filter, falling fuzzy implicative filter, falling fuzzy G-filter, falling fuzzy positive implicative filter, residatued lattice, falling fuzzy Boolean filter

CLC Number: 

  • TP18
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