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.
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Zhang, Jl. Fuzzy prime Boolean filters and their operations in IMT L-algebras. Fuzzy Inf. Eng. 1, 401–419 (2009). https://doi.org/10.1007/s12543-009-0031-z
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DOI: https://doi.org/10.1007/s12543-009-0031-z