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Fuzzy prime Boolean filters and their operations in IMT L-algebras

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  • Jia-lu Zhang

    (Xiangnan University)

Abstract

Some characterizations of fuzzy prime Boolean filters of IMT L-algebras are given. The lattice operations and the order-reversing involution on the set PB(M) of all fuzzy prime Boolean filters of IMT L-algebras are defined. It is showed that the set PB(M) endowed with these operations is a complete quasi-Boolean algebra (a distributive complete lattice with an order-reversing involution). It is derived that the algebra M=F, which is the set of all cosets of F, is isomorphic to the Boolean algebra {0; 1} if F is a fuzzy prime Boolean filter. By introducing an adjoint pair on PB(M), it is proved that the set PB(M) is also a residuated lattice.

Suggested Citation

  • Jia-lu Zhang, 2009. "Fuzzy prime Boolean filters and their operations in IMT L-algebras," Fuzzy Information and Engineering, Springer, vol. 1(4), pages 401-419, December.
    • Handle: RePEc:spr:fuzinf:v:1:y:2009:i:4:d:10.1007_s12543-009-0031-z
    DOI: 10.1007/s12543-009-0031-z
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