FUZZY FILTERS ON THE RESIDUATED LATTICES

Jia-Lu Zhang () and Hong-Jun Zhou ()
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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

New Mathematics and Natural Computation (NMNC), 2006, vol. 02, issue 01, 11-28

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.

Keywords: Residuated lattice; regular residuated lattice; fuzzy filter; fuzzy filter lattice; fuzzy strong-prime filter; quasi-Boolean algebra (search for similar items in EconPapers)
Date: 2006
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DOI: 10.1142/S1793005706000373

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