不确定性概念的描述与处理是人工智能研究中的一个基础问题。人们已经提出了概率论、模糊集、粗糙集、云模型等诸多理论模型来解决这一问题。人类基于词语（概念内涵）处理不确定性概念，而计算机基于样本集合（概念外延）处理不确定性概念。本申请项目拟结合粗糙集和云模型，研究基于内涵的计算和基于外延的计算之间的联系，建立一个双向认知计算模型。主要研究内容有：建立基于云模型的概念内涵与外延之间的稳定双向映射计算模型；探究基于内涵的逻辑运算与基于外延的集合运算之间的对应关系及相互转换机制；研究不同概念层次思维（推理）的多粒度（变粒度）计算模型；用云模型的正向/逆向发生器生成粗糙集的上、下近似集，建立随机粗糙集理论模型，解决粗糙集的过度学习和弱泛化能力问题，从而实现多粒度双向认知计算。本项目的研究成果，可实现人类认知行为的计算模拟，并为描述处理不确定性概念提供新的理论方法，推动不确定性人工智能的发展。

The expressing and processing of uncertain concetpts is a fundamental problem in artificial intelligence. Several theoretical models have been proposed for solving this problem, such as probability theory, fuzzy sets, rough sets, cloud model, et al. Human deals with uncertain concepts based on words(concept intension), while computer based on sample set(concept extension). This project tries to study the relationship between the intension based computing and the extension based computing through integrating the rough sets theory and cloud model, and develop a bidirectional cognitive computing model.Its key research points are: develop a stable bidirectional mapping cloud model between the intension and extension of concepts; study the mapping relation between the intension based logic reasoning and the extension based set operation, and their mutual transformation mechanism; study the multi-granularity (variable granularity) computing model for simulating hierachical thinking (reasoning); develop a random rough set theory model, which is a multi-granularity bidirectional cognitive computing model, to solve its limitations of over training and weak generalization ability, through generating its lower and upper approximations using the forward/backward cloud generators. The research results of this project could realize the computer simulation of human cognitions and provide a new theoretical model for expressing and processing uncertain concepts. It will push the development of artificial intelligence with uncetainty.