Abstract
In this chapter, we discuss some issues related to lattice implication algebras. In Sections 8.1 and 8.2, we establish the categories of lattice implication algebras and fuzzy lattice implication algebras and discuss their basic properties. In Section 8.3 we presented the fuzzy power sets theory based on lattice implication algebras, which is a generalization of Bandler and Kohout’s fuzzy power sets theory. In Section 8.4, we discuss the properties of semigroups (L, ⊕), (L, ⊗) and adjoint semigroup (M(L), o, 1 L ), they are induced by a lattice implication algebra L. In Section 8.5, we formalize lattice implication algebra system in a first-order language with identity and study the logical properties of this algebra.
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© 2003 Springer-Verlag Berlin Heidelberg
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Xu, Y., Qin, K., Ruan, D., Liu, J. (2003). Related Issues. In: Lattice-Valued Logic. Studies in Fuzziness and Soft Computing, vol 132. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-44847-1_8
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DOI: https://doi.org/10.1007/978-3-540-44847-1_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-07279-6
Online ISBN: 978-3-540-44847-1
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