【作者】 杨凯；

【导师】 陈俊杰；

【作者基本信息】 太原理工大学 ， 计算机应用技术， 2007， 硕士

【摘要】 在不同的抽象层次上观察、理解、表示现实世界问题连同其解，并进行分析、综合、推理，是人类问题求解过程的一个明显特征，也是人类问题求解能力的强有力的表现。从一定意义上来说，这就是人类问题求解过程中智能之所在。针对人类问题求解的这种能力和特征，人工智能研究者对其进行了深入的研究，并建立了各种形式化的模型。作为一种正在兴起的人工智能研究领域，粒计算的目的就是建立一种体现人类问题求解特征的一般模型，其基本思想是在不同的粒度层次上进行问题求解。商空间理论，用三元组（x，f，T）描述一个所要解决的问题。其中X表示问题的论域；f：X→Y表示论域的属性；T是论域的结构，即指论域中各元素的相互关系。分析或求解问题（X，f，T），就是对论域X及其有关的结构、属性进行分析、研究。很大一类推理问题都可以归结为一个对应的与或图上的搜索过程。商空间理论描述的与或图推理模型对于信息的不确定性，是通过建立不同粒度层次的方式来解决的。但是很多情况下需要研究的粒度层次会出现无法避免的不确定性。于是，就需要对原有模型进行扩展，构建对于不确定性粒度的描述方式，形成推广的与或图推理模型。本文将模糊集理论中对粒度描述的方法引入到商空间描述的与或图推理模型（（X，D），（f，g），（?），F₁，F₂，（A，p））中。用模糊的粒度描述A_F、p_F代替清晰的粒度描述A、p，在此基础上构建适当的属性函数f_F和推理函数g_F，形成模糊与或图推理模型（（X，D），（f_F，g_F），（?），F₁，F₂，（A_F，p_F））。同时，证明了模糊的与或图推理模型在商空间理论下的投影与合成的可行性。对于商空间下的推理模型（（X，D），（f_F，g_F），（?），F₁，F₂，（A_F，p_F）），构造论域X的商集X₁。可以证明按照商空间理论的基本原理，能够推导出原模型的投影模型(（X₁，D₁），(f_F1，g_F1)，（?），F₁，F₂，(A_F1，p_F1))。对于两个与或结构的商空间模型(（X₁，D₁），(f_F1，g_F1)，（?），F₁，F₂，(A_F1，p_F1))，(（X₂，D₂），(f_F2，g_F2)，（?），F₁，F₂，(A_F2，p_F2))可以使用首先将与或图化成某种对应的或图进行合成，然后再将合成的或图变换到对应的与或图的方法，求解出原模型的合成推理模型(（X₃，D₃），(f_F3，g_F3)，（?），F₁，F₂，(A_F3，p_F3))。在此基础上，利用构造的模糊商空间下的与或图推理模型，求解皮肤敏感试验模拟问题。通过对求解问题构建商空间的描述，将问题转化为在模糊粒度描述的与或图上搜索节点的过程。在求解过程中利用商空间下的投影与合成理论，在不同的商空间上变换，使用模糊集的粒度描述方法，解决了问题中的不确定性因素，最终解决问题。不仅验证了构建的模糊商空间下的与或图推理模型的正确性，同时也为医学上对头孢菌素复方药物的过敏性研究提供了一种处理不确定性因素的模型与思路。更多还原

【Abstract】 Observation, understanding and representation, as well as analysis, synthesis and reasoning, of real world problem together with its solution at different levels of granularity, is an obvious feature in the process of human problem solving, and it also embodies the outstanding ability of human problem solving. In a sense, it is the intelligence in the process of human problem solving. Considering such ability of human, researchers of artificial intelligence have made some further investigation and presented many formal models. As an emerging research sub-field of artificial intelligence, granular computing, whole philosophy is to implement the problem solving at different levels of granularity, aims to establish much more general model reflecting the process of human problem solving.In quotient space theory, triplet （X,f,T） is proposed to describe a problem space, where X denotes the universe; f: X→Y indicates the attributes （or features） of universe X; an d T is the structure of universe X, na mely the relationship of different items at universe X. The resolving problem （X,f,T） is the process of analyzing and researching the universe X, the attributes f and the structure T.A great sort of problems can be summed up as a process of searching nodes on a corresponding and/or graphic. And/or reasoning model under quotient space solves uncertainty of information though the approach of setting different granule levels. But many times, some uncertainties of the granules which need to be studied cannot be avoided. The foregoing model needs to be extended to a new one which is capable of describing uncertain granules.This paper introduces the approach of describing granules in fuzzy set into processing and/or graphic reasoning model under quotient Space theory. Uses fuzzy definitions A_F and P_F instead of A and p .based on this, constructs corresponding property function f_F and reasoning function g_F, form the integrated fuzzy and/or reasoning model （（X, O）, （f_F, g_F）,（?）, F₁, F₂, （A_F, P_F）） .Meanwhile, the paper improves fuzzy and/or graphic reasoning model is capable of projecting and combining in different quotient spaces levels. For reasoning model （（X,D）,（f_F,g_F）,（?）,F₁,F₂,（A_F,P_F））, defines X₁ as the quotient set of universe X ,and the projection model (（X₁,D₁）,(f_F1,g_F1),（?）,F₁,F₂,(A_F1,P_F1) can be built. For two reasoning models (（X₁,D₁）,(f_F1,g_F1),（?）,F₁,F₂,(A_F1,P_F1) and (（X₂,D₂）,(f_F2,g_F2),（?）₂,F₁,F₂,(A_F2,p_F2), transforms the and/or graphics to the corresponding or graphics, combines them to a new model, and transforms it into a corresponding and/or graphic, then constructs the combination model (（X₃, D₃）, (f_F3, g_F3), （?）₃, F₁, F₂,(A_F3, P_F3).Finally, based on fuzzy and/or graphic reasoning model under quotient. space theory, the paper solves a simulative dermal sensitivity test question. Through constructs quotient space description of the question, transforms the question into a process of searching fuzzy nodes on and/or graphic. The approach solves uncertainty by utilizing the projection and combination of fuzzy and/or graphic model between different quotient spaces. Not only testifies validity of fuzzy and/or graphic reasoning model, but also provides a new mode of disposing uncertainty in medical research on cephalosporin allergy更多还原