布尔算子Fuzzy逻辑中的锁归结原理

本文将一阶逻辑中的锁归结方法和广义锁归结方法推广到布尔算子Ｆｕｚｚｙ逻辑中，并且证明了布尔算子Ｆｕｚｚｙ逻辑的锁归结方法和一种特殊的广义锁归结方法是广义完备的。     

算子Fuzzy逻辑及其归结推理的改进

在文献[3],[7]基础上,重新定义了算子格中的算子对格元素的作用,并引进了结合算子格的概念,改进了算子Fuzzy逻辑。为限定词的表示提供了一个模型。在新的系统中,引进了α-解释和λ_α-恒假概念,从而引进λ_α-归结方法。     

基于Rough集的Rough数及入算子的逻辑价值*

本文在介绍Rough集基础上，提出了基于Rough集理论的Rough数概念及其运算法则．并给出了这种Rough数应用实例及其近似程度算子λ在Rough逻辑中的理论价值．     

基于Rough集的Rough数及λ算子的逻辑价值

本文在介绍Ｒｏｕｇｈ集基础上，提出了基于Ｒｏｕｇｈ集理论的Ｒｏｕｇｈ数概念及其运算法则，并给出了这种Ｒｏｕｇｈ数应用实例及其近似程度算子λ在Ｒｏｕｇｈ逻辑中的理论价值。     

算子动态模糊逻辑系统及其归结研究

主要讨论了一种只包含动态模糊算子和动态模糊文字的算子动态模糊逻辑系统,介绍了该系统的逻辑性质,在系统中定义了其λ-归结。     

归结原理及其应用

归结演绎推理是一种在计算机上得到较好实现的基于归结原理的推理技术,介绍归结原理的基本思想以及它在自动推理中的应用。     

布尔算子Fuzzy逻辑中归结的广义完备性

本文在布尔算子Ｆｕｚｚｙ逻辑中引入公式的恒假水平的概念，证明了归结原理在定性和定量这两种度量意义下的广义完备性。     

算子Fuzzy逻辑和λ—归结方法

本文提出了算子Fuzzy逻辑,并给出了这种逻辑系统中公式的一些简单性质,在算子Fuzzy逻辑中,提出了λ-恒真和λ-恒假的概念,提出了λ-归结方法。证明了:对于任一个λ-恒假公式,使用λ-归结方法,都可以在有限步内,给以判定。     

布尔算子Fuzzy逻辑中的锁归结原理*

本文将一阶逻辑中的锁归结方法和广义锁归结方法推广到布尔算子Fuzzy逻辑中，并且证明了布尔算子Fuazzy逻辑中的锁归结方法和一种特殊的广义锁归结方法是广义完备的．     

使用XML的一阶谓词逻辑归结原理

归结原理（resolution principle)是计算机自动推理的重要原理之一。将XML加入到使用归结原理的证明过程中，利用XML结构与语义自描述的特性，简化归结过程的计算机实现，并给出相应基于XML的算法。     

基于Rough集的模态逻辑及其近似推理

本文在Ｒｏｕｇｈ集上定义模态逻辑,并将这种逻辑的真值解释在Ｒｏｕｇｈ集上,使得古黄模态逻辑的必然和可能真值统一为Ｒｏｕｇｈｌｙ真值。文章还阐述了这种真值在近似推理中的应用。     

近似精度Rough数及其在DSS中的应用

本文在介绍Ｒｏｕｇｈ集基础上，用Ｒｏｕｇｈ下和上近似集定义了近似精度Ｒｏｕｇｈ数及其运算法则。并举例说明了这种新构想的Ｒｏｕｇｈ数被应用于ＤＳＳ（决策支持系统）中颇有新意。最后，阐述了近似精度μ将使Ｒｏｕｇｈ逻辑的五值被扩充为多值。     

A ROUGH SET/FUZZY LOGIC BASED DECISION MAKING SYSTEM FOR MEDICAL APPLICATIONS

Abstract

A method of performing prognostic modeling of disease states is proposed. The technique uses rough sets to extract rules from a database. The data is then reformatted into a fuzzy logic template, and a learning algorithm is used to adjust the fuzzy set membership functions. The method is applied to the POSCH problem, which looks at risk factors associated with the progression of coronary artery disease. The POSCH data has several shortcomings, including a limited number of cases, correlated inputs, as well as noise on both the inputs and outcome. The problem was to predict progression of atherosclerosis in the LAD three years after baseline based on physiologic data available at baseline. The proposed rough/fuzzy set method correctly predicted progression of atherosclerotic disease in 69% of the patients, which is statistically better than neural network, rough set and logistic models performed.     

带Rough算子的决策规则及数据挖掘中的软计算

文中讨论决策规则及其与演绎推理中的假言推理规则之间的关系,通过数据挖掘中的软计算使决策表中的属性简化和性值区间化,从而找到一种具有广泛表达能力的数据隐含格式,从中选择有代表性的,并删去冗余或过剩的规则,并保持决策表的原有用途和的有性能,我们通过开发一个中医诊疗专家系统的实例说明了这种软计算的过程,并分别用于统计或专家计算带可信度因子的产生式规则和基于Ｒｏｕｇｈ集方法计算带Ｒｏｕｇｈ算子的决策规则两     

基于算子模糊逻辑的不确定程度计算

本文提出并比较了在信度语义下，计算算子模糊逻辑中公式（集）模糊程度的3种方法——归结法、广义归结法和TABLEAU方法．     

ROUGH FUZZY SETS AND FUZZY ROUGH SETS*

The notion of a rough set introduced by Pawlak has often been compared to that of a fuzzy set, sometimes with a view to prove that one is more general, or, more useful than the other. In this paper we argue that both notions aim to different purposes. Seen this way, it is more natural to try to combine the two models of uncertainty (vagueness and coarseness) rather than to have them compete on the same problems. First, one may think of deriving the upper and lower approximations of a fuzzy set, when a reference scale is coarsened by means of an equivalence relation. We then come close to Caianiello's C-calculus. Shafer's concept of coarsened belief functions also belongs to the same line of thought. Another idea is to turn the equivalence relation into a fuzzy similarity relation, for the modeling of coarseness, as already proposed by Farinas del Cerro and Prade. Instead of using a similarity relation, we can start with fuzzy granules which make a fuzzy partition of the reference scale. The main contribution of the paper is to clarify the difference between fuzzy sets and rough sets, and unify several independent works which deal with similar ideas in different settings or notations.     

VAGUENESS AND UNCERTAINTY: A ROUGH SET PERSPECTIVE

Vagueness and uncertainty have attracted the attention of philosophers and logicians for many years. Recently, AI researchers contributed essentially to this area of research. Fuzzy set theory and the theory of evidence are seemingly the most appealing topics. On this note we present a new approach, based on the rough set theory, for looking to these problems. The theory of rough sets seems a suitable mathematical tool for dealing with problems of vagueness and uncertainty. This paper is a modified version of the author's lecture titled "An inquiry into vagueness and uncertainty," which was delivered at the AI Conference in Wigry (Poland), 1994.     

基于粗糙集的神经网络建模方法研究

提出了一种基于粗糙集的神经网络模型,该方法利用粗糙集数据分析方法,从数据中提取出规则将输入映射到输出的子空间上,而后在这个子空间上用神经网络进行逼近.利用这种方法对岩石边坡工程中边坡稳定性进行分析建模,并和传统的神经网络建模方法进行比较,说明了该方法的有效性.     

直觉模糊粗糙推理的规则库完备性研究

针对规则库检验问题,提出了直觉模糊粗糙规则库的完备性检验方法.首先,引入直觉模糊粗糙集的概念,给出了直觉模糊粗糙规则库的完备性定义;其次,针对直觉模糊粗糙规则库的完备性,提出了完备性检验算法,指出如何设计规则库才能满足完备性要求;最后,通过实例验证了算法的合理性和有效性.     

Rough集及在近似推理中的应用

本文介绍了Ｒｏｕｇｈ集的基本概念,阐述了Ｒｏｕｇｈ集与信息系统之间的关系,构造了一个基于Ｒｏｕｇｈ近似的距离函数,并使属性值区间化,且略述了开发的中医诊断专家系统,最后,展望了Ｒｏｕｇｈ集的研究前景。