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

Jia-lu Zhang ()
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Jia-lu Zhang: Xiangnan University

Fuzzy Information and Engineering, 2009, vol. 1, issue 4, 401-419

Abstract: 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.

Keywords: IMT L-algebra; Fuzzy filter; Fuzzy prime Boolean filter; Residuated lattice; Quasi-Boolean algebra (search for similar items in EconPapers)
Date: 2009
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DOI: 10.1007/s12543-009-0031-z

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