不确定性信息表示及推理

在基于数据的复杂系统建模过程中,各种不确定性信息普遍存在.一般而言,客观系统的随机性与人类认知的模糊性构成了不确定性的最基本内涵.为了对不确定性信息进行形式化的描述,促进人类对实际系统的理解,近年来各种不确定性理论得到极大发展.基于此,首先给出不确定性的来源、分类及特点;然后,从随机性、模糊性及混合不确定性3方面系统梳理贝叶斯推理、模糊推理、粗糙集、灰色理论和证据理论等方法在不确定性信息表示与推理方面的研究,同时总结分析上述理论在可靠性工程、信息融合和决策支持等方面的典型应用;最后,在对现有工作简要总结的基础上,提出不确定性理论在未来发展中面临的三大挑战,并给出潜在的解决思路,以期为该领域的研究者提供一定的参考.

Expression and inference of uncertain information

In the process of modeling complex systems based on data, a large amount of uncertain knowledge prevails. Generally, the randomness of the objective system and the ambiguity of human cognition constitute the basic connotation of uncertainty. To formally describe the uncertain information and promote human understanding of the actual system, various uncertain theories have been greatly developed in recent years. Therefore, the source, classification and characteristics of uncertainty are firstly given. Then, from the randomness, fuzziness and mixed uncertainty, this paper systematically summarizes the researches of Bayesian inference, fuzzy inference, rough set, grey theory and evidence theory on the expression and inference of uncertain information. The typical applications of the above theories in engineering practice are discussed from three aspects: reliability engineering, information fusion and decision support. Finally, based on a brief summary of the existing work, three major challenges faced by uncertainty theory in the future development are proposed, and potential solutions are given to provide some reference for researchers in this field.