【作者】 朱华；

【导师】 徐扬；

【作者基本信息】 西南交通大学 ， 基础数学， 2005， 硕士

【摘要】 格值逻辑系统为智能信息处理提供了一种逻辑基础。格蕴涵代数作为一种重要的逻辑代数,为格值逻辑和不确定性推理的研究提供了一种理论基础。本文基于格蕴涵代数已有的性质,进一步讨论了滤子、模糊滤子和理想的性质,以期对格值逻辑系统提供一定的理论基础。本文主要取得以下结果: 1.研究了格蕴涵代数和剩余格之间的关系,得到了剩余格蕴涵代数和正则剩余格等价的结论。利用格蕴涵同态映射研究格蕴涵代数的识别,从而得到由已有的格蕴涵同态映射构造新格蕴涵代数的方法。 2.在剩余格蕴涵代数中,提出了滤子的根、准素滤子和n-重素滤子的概念,并讨论了其相关性质和它们之间的关系。给出了剩余格蕴涵代数中对不同的自然数n,n-重关联滤子之间的关系,和n-重正关联滤子之间的关系。 3.提出了n-重模糊关联滤子的概念,研究了它的性质,讨论了它与模糊滤子和n-重关联滤子之间的关系,以及对不同的自然数n,n-重模糊关联滤子之间的关系。 4.提出了n-重模糊正关联滤子的概念,研究了它的性质,讨论了它与模糊滤子、n-重正关联滤子和n-重模糊关联滤子之间的关系,以及对不同的自然数n,n-重模糊正关联滤子之间的关系。 5.提出了n-重模糊结合滤子的概念,研究了它的性质,讨论了它与模糊滤子、n-重结合滤子和n-重模糊关联滤子之间的关系,以及对不同的自然数n,n-重模糊结合滤子之间的关系。 6.提出了理想的根、准素理想的概念,研究了其性质,并讨论了它们之间的关系及与理想之间的关系。提出了零化子的概念,证明了零化子是理想,并给出了零化子的一些特殊性质。更多还原

【Abstract】 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更多还原