粗糙逻辑中公式的Borel型概率粗糙真度

以一种特殊的粗糙逻辑为研究对象，视全体赋值之集为通常乘积拓扑空间，通过利用赋值集上的Borel概率测度，提出了能融合粗糙逻辑与计量逻辑为一体的公式的Borel型概率粗糙真度理论，给出了公式概率粗糙真度的公理化定义，建立起了相应的概率真度表示定理.公式的概率粗糙真度理论可被看作粗糙逻辑中已有工作的计量化，也可看作计量逻辑学中真度理论的粗糙化.基于这一核心概念，进一步给出了粗糙逻辑中已有概念的程度化表示形式，如公式的粗糙度、精确度、公式之间的粗糙相似度等，并建立起了基于粗糙相似度的3种近似推理模式.该结果实现了粗糙逻辑与计量逻辑的和谐统一，为进一步基于粗糙真值的程度化推理搭建了一个可能的框架.

Borel Probabilistic Rough Truth Degree of Formulae in Rough Logic

This paper introduces the notion of the Borel probabilistic rough truth degree of a formula in a special kind of rough logic, by employing Borel probability measures on the valuation set endowed with the usual product topology. It facilitates a special form of rough logic with integration to quantitative logic. The axiomatic definition of probabilistic rough truth degree is given and its representation theorem is also presented. The proposed notion of Borel probabilistic rough truth degree can be regarded as the quantitative analysis of rough logic, as well as the advancing research of the existing notion of truth degree from rough set perspective. Based upon the fundamental notion of rough truth degree, some graded versions of the existing notions, including the roughness degree, accuracy degree and the rough similarity degree, are also presented. Subsequently, three different kinds of approximate reasoning models are established. The obtained results achieve a combination of rough logic and quantitative logic and provide a possible framework for rough truth based approximate reasoning.