粗糙逻辑中公式的一种新的粗糙概率真度

本文以任意预粗糙代数为赋值格的粗糙逻辑为研究对象，基于格赋值理论，通过在预粗糙代数赋值格和全体公式集上分别建立概率测度，利用积分方法提出了粗糙逻辑中公式的一种新的粗糙概率真度.证明了粗糙概率真度的MP规则、HS规则和交推理规则，同时引入了公式的精确度和粗糙度的概念.基于粗糙概率真度，提出公式间的9种粗糙相似度和伪距离，进而提出3种近似推理模式，研究了相关性质.将计量逻辑学中的相关理论推广到以预粗糙代数为赋值格的粗糙逻辑上，为基于粗糙概率真度的程度化推理提供了一种可能的框架.

New Type of Rough Probabilistic Truth Degree of Formulae in Rough Logic

In this paper,based on lattice evaluation theory and by defining probality measure in pre-rough algebra evaluation lattice and set of all formulae respectively,the new type of rough probabilistic truth degree of formulae in rough logic is introduced by the integral method.The MP rule,HS rule and meet inference of rough probabilistic truth degree are proved,the concept of accuracy degree and roughness degree of fomulae are introduced also.At the meantime,the concept of rough similarity degree and pseudo-distances between formulae are introduced and three different kinds of approximate reasoning models are estabished.The theory of quantitative logic is expanded to rough logic,which makes it possible in graded reasoning in rough logic.