基于剩余格的具有内态的模糊逻辑研究

项目名称： 基于剩余格的具有内态的模糊逻辑研究

项目编号： No.61273017

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 自动化技术、计算机技术

项目作者： 刘练珍

作者单位： 江南大学

项目金额： 56万元

中文摘要： 将T.Flaminio和F.Montagna内态的思想引入到基于左连续三角模的模糊逻辑及非可换代数系统， 建立态IMTL－代数、态MTL－代数及具有内态的非可换代数系统， 研究它们的基本性质；在上述代数系统中提出态滤子、素态滤子、极大态滤子、布尔态滤子及蕴涵态滤子的概念，研究它们的性质及刻画；研究态滤子和同余之间的关系；讨论布尔态滤子及蕴涵态滤子之间的关系；研究布尔态滤子和bipartite态IMTL－代数、bipartite 态MTL－代数的关系；研究极大态滤子和局部态IMTL－代数、局部态MTL－代数的关系。研究子直积不可约的态射IMTL－代数和态射MTL－代数的结构。建立具有内态的逻辑系统，研究其可靠性及完备性。 本研究是非经典逻辑领域的一个创新性研究， 此学科交叉研究会带来很多很有意义的研究课题。同时， 基于剩余格的模糊逻辑研究在模糊控制、人工智能、模糊逻辑规划等领域有着很好应用。

中文关键词： 态IMTL-代数；剩余格；滤子；Riecan 态；伪准相等

英文摘要： We apply T.Flaminio and F.Montagna's idea to left continuous t-norm based fuzzy logics and noncommutative algebras and establish the systems of IMTL-algebras with internal states, MTL-algebras with internal states and noncommutative algebras with internal states. Some fundamental properties on these algebras are also obtained. The notions of state filters, prime state filters , maximal state filters, Boolean state filters and implicative state filters are introduced on the above algebras and some properties and characteristics of state filters, prime state filters, maximal state filters, Boolean state filters and implicative state filters are obtained respectively. The relations between state filters and congruences, between Boolean state filters and implicative state filters are discussed. Moreover, the relations between Boolean state filters and bipartite state IMTL-algebras,between Boolean state filters and bipartite state MTL-algebras,between maximal state filters and local state IMTL-algebras,between maximal state filters and local state MTL-algebras are investigated. Furthermore, we introduce the notions of state-morphism IMTL-algebras and state-morphism MTL-algebras and study some of their properties. We also study subdirectly irreducible state-morphism IMTL-algebras and subdirectly irreducible state-mo

英文关键词： State IMTL-algebra；Residuated lattice；Filter；Riecan state；Pseudo-quasi-equivalent