Study On Filters And Ideals Of Lattice Implication Algebra

Lattice-valued logic system supplys a logic foundation for intelligent information processing. As an important logical algebra, lattice implication algebra offers a theoretical basis for lattice-valued logic and approximate reasoning. Based on the existing results of lattice implication algebra, the properties of filters, fuzzy filters and ideals are further discussed in this paper, in order to provide certain theoretical basis for lattice-valued system. The main results of this paper are listed as follows.1.Studied the relationship between lattice implication algebra and residuated lattice, and obtained the conclusion that residuated lattice implication algebra is equivalent to regular residuated lattice. Studied the identification of lattice implication algebra by using the lattice implication homomorphism, and obtained the methods of forming new lattice implication algebra based on the existed lattice implication homomorphism.2.Proposed the concepts of filter's radical, primary filter and n-fold prime filter in residuated lattice implication algebra, and discussed the related characteristics and the relations among them. For different n, the relations among n-fold implicative filters are given in residuated lattice implication algebra and so are n-fold positive implicative filters.3.Proposed the notion of n-fold fuzzy implicative filter, then studied its propositions. The relations among fuzzy filter, n-fold implicative filter and for different n, n-fold fuzzy implicative filter are also discussed.4.Proposed the notion of n-fold fuzzy positive implicative filter, then studied its propositions. The relations among fuzzy filter, n-fold positive implicative filter and n-fold fuzzy implicative filter and for different n, n-fold fuzzy positive implicative filter are also discussed.5.Proposed the notion of n-fold fuzzy associative filter, then studied its propositions. The relations among fuzzy filter, n-fold associative filter and n-fold fuzzy implicative filter and for different n, n-fold fuzzy associative filter are also...