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Fuzzy Filters On The Residuated Lattices

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  • JIA-LU ZHANG

    ()
    (Department of Mathematics, Xiangnan University, Chenzhou, Hunan, 423000, P. R. China)

  • HONG-JUN ZHOU

    ()
    (Institute of Mathematics, Shanxi Normal University, Xi'an, 710062, P. R. China)

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    Abstract

    In this paper, the lattice operations and the adjoint pair on the fuzzy filters set on residuated lattices are defined, the conclusion that the fuzzy filters lattice defined as such is a distributive residuated lattice is obtained. An order-reversing involution on the fuzzy strong-prime filters sublattice is introduced. It is proved that the fuzzy strong-prime filters sublattice is a quasi-Boolean algebra.

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    Bibliographic Info

    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal New Mathematics and Natural Computation.

    Volume (Year): 02 (2006)
    Issue (Month): 01 ()
    Pages: 11-28

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    Handle: RePEc:wsi:nmncxx:v:02:y:2006:i:01:p:11-28

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    Related research

    Keywords: Residuated lattice; regular residuated lattice; fuzzy filter; fuzzy filter lattice; fuzzy strong-prime filter; quasi-Boolean algebra;

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