基于两类超逻辑代数的不确定性研究

The hyper structures of logical algebras are important branches of logical algebras, which have already been deeply applied to intelligent information processing fields. This project is focused on investigating two classes of hyper logical algebras, that is, hyper BL-algebras and hyper R0-algebras, and discussing their corresponding non-classical logical reasoning systems and uncertainty reasoning methods. This project mainly includes the following topics: the structures of hyper BL-algebras and hyper R0-algebras are established and some soft set theory and falling fuzzy theory based on these two kinds of hyper logical algebras are described, respectively. The topological hyper BL-algebras and topological hyper R0-algebras are constructed and their quotient strctures are discussed. Moreover, some properties of fuzzy hyper filters and fuzzy hyper ideals are considered. Applied fuzzy set theory, rough set theory and soft set theory to hyper BL-algebras and hyper R0-algebras, some structures and properties of soft fuzzy rough hyper filters and soft rough fuzzy hyper filters are discussed. The non-classical logical reasoning systems-HBL reasoning systems and HL* reasoning systems corresponding to hyper BL-algebras and hyper R0-algebras are established, respectively, and the relationships among them are discussed.Also,uncertainty reasoning methods based on HBL reasoning systems and HL* reasoning systems are investigated. Through the research of this project, it is expected that some fuzzy logical systems based on t-norms will be extended to non-classical logical reasoning systems based on hyper algebraic structures, and a new method for uncertainty reasoning methods based on hyper algebraic structures will be established. It will provide the algebraic and logical foundations for more general intelligent information processing.

逻辑代数的超结构是逻辑代数的一个重要分支，已深入应用于智能信息处理领域。本项目重点研究两类超逻辑代数（超BL-代数与超R0-代数），并探讨与之配套的非经典逻辑系统及不确定推理方法，主要包括：建立超BL-代数与超R0-代数理论以及研究软集理论和落影理论；构造拓扑超BL-代数与拓扑超R0-代数，研究其商结构，并刻画其模糊超滤子与模糊超理想；将模糊集，粗糙集与软集三者结合，运用到超BL-代数与超R0-代数中，并研究这两类超逻辑代数的软模糊粗糙超滤子和软粗糙模糊超滤子；分别建立与超BL-代数、超R0-代数相配套的逻辑系统--HBL系统与HL*系统，研究其相互联系，并探讨基于HBL系统与HL*系统的不确定推理方法。通过本项目的研究，将若干基于t-模的模糊逻辑系统拓广为基于超代数结构的非经典逻辑系统，并建立基于超代数结构的不确定推理新方法，为更具一般性的智能信息处理提供代数与逻辑基础。

逻辑代数的超结构是逻辑代数的一个重要分支，已深入应用于智能信息处理领域。本项目重点研究两类超逻辑代数（超BL-代数与超R0-代数），并探讨与之配套的非经典逻辑系统及不确定推理方法，主要包括：建立超BL-代数与超R0-代数理论以及研究软集理论和落影理论；构造拓扑超BL-代数与拓扑超R0-代数，研究其商结构，并刻画其模糊超滤子与模糊超理想；将模糊集，粗糙集与软集三者结合，运用到超BL-代数与超R0-代数中，并研究这两类超逻辑代数的软模糊粗糙超滤子和软粗糙模糊超滤子；分别建立与超BL-代数、超R0-代数相配套的逻辑系统——HBL 系统与HL*系统，研究其相互联系，并探讨基于HBL系统与HL*系统的不确定推理方法。通过本项目的研究，将若干基于t-模的模糊逻辑系统拓广为基于超代数结构的非经典逻辑系统，并建立基于超代数结构的不确定推理新方法，为更具一般性的智能信息处理提供代数与逻辑基础。