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Fuzzy Filters On The Residuated Lattices


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


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

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


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