JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2014, Vol. 49 ›› Issue (12): 87-94.doi: 10.6040/j.issn.1671-9352.0.2014.325

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Fuzzy ultra ⊙-ideals in regular residuated lattices

LIU Chun-hui1,2   

  1. 1. Office of Teaching Affair, Chifeng University, Chifeng 024001, Inner Mongolia, China;
    2. Department of Mathematics and Statistics, Chifeng University, Chifeng 024001, Inner Mongolia, China
  • Received:2014-07-15 Revised:2014-10-21 Online:2014-12-20 Published:2014-12-20

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Abstract: Firstly, the notion of fuzzy ultra ⊙-ideal is introduced and its properties are investigated in regular residuated lattices, and some equivalent characterizations of fuzzy ultra ⊙-ideals are obtained. Secondly, the lattice operations ∨, ∧ and the order-reversing involution on the set FU(L) of all fuzzy ultra ⊙-ideals in a regular residuated lattice L are defined. It is proved that (FU(L),∨,∧,,0L,1L) formes a De Morgan algebra if L satisfies the condition (P). Finally, the adjoint pair () on FU(L) is defined. It is also proved that (FU(L),,0L,1L) formes a residuated lattice if L satisfies the condition (P).

Key words: fuzzy logic, fuzzy ⊙-ideal, fuzzy ultra ⊙-ideal, De Morgan algebra, (regular)residuated lattice

CLC Number: 

  • O141.1
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