多粒度信息的多值逻辑描述及其计量化知识推理

项目名称： 多粒度信息的多值逻辑描述及其计量化知识推理

项目编号： No.61472471

项目类型： 面上项目

立项/批准年度： 2015

项目学科： 其他

项目作者： 折延宏

作者单位： 西安石油大学

项目金额： 58万元

中文摘要： 与粒计算所倡导的多视角、多层次的信息处理观点相适应，目前，基于不完备与不精确信息的逻辑推理已由单粒度转向多粒度。然而，在多粒度信息环境下，作为其语义理论中的核心概念,粗糙集将论域划分为三个互不相交的区域，即正域、边界域和负域，所对应的逻辑真值分别为1，1/2，0。因此，这种多粒度逻辑推理仍然是在三值逻辑的框架下展开的。鉴于此，本项目拟利用粗糙隶属度函数，将边界域元素按其粗糙隶属度进一步细分，将公式在局部环境下的判断由三值转变为多值。基于此，利用概率测度论，将局部判断下公式所对应的全体赋值进行集成，引入公式粗糙为真、公式间粗糙相等等诸多概念的程度化判断，建立起以逻辑公式为元素的粗糙逻辑度量空间，并给出相应的不确定性推理方法。进一步，将不同粒度及其所对应的二元关系融入到如上给出的逻辑度量空间中，通过将它们之间的知识包含等程度化，最终建立起融合概率论、多值逻辑及粗糙集为一体的计量化推理模式。

中文关键词： 粗糙集；多粒度；多值逻辑；知识推理

英文摘要： To adapt to the multiview and multilevel information processing initiated by granular computing, presently,the logical reasoning based on incomplete and imprecise information has been extended from single granulation to multigranul- ation.However, in the context of multigranular information, since rough set,a key notion in the semantic theory, divides the universe into three disjoint parts, namely,positive region, boundary region and negative region with corresponding truth values1,1/2 and 0, the existing logical reasoning corresponding to multigranular information is mainly conducted in the context of three-valued logic.Taking this fact into consideration, this project aims to transform the three-valued descrip- tion of local judgement into a multiple-valued one by subdividing the elements in the boundary region using rough membership functions.Based on this,the concepts such as rough truth, rough equality and the like are all graded by using probability measure theory, more specifically, by integrating all the valuations under the local judgement.Consequently,a kind of rough logic metric space consisting of logic formu- lae is obtained and the corresponding uncertainty reasoning method is presented. Moreover,by putting different granulations and their relations into the framework of logic metric space and grading their knowledge dependency,etc.,a kind of quantitative reasoning framework combining probability theory, multiple-valued logic and rough set can be finally established.

英文关键词： rough set;multigranulation;multiple-valued logic;reasoning about knowledge