不确定性集合理论及其研究进展

Uncertainty set theory and its research development

目的介绍Fuzzy集、Vague集和Rough集等理论,揭示它们之间的关系,在总结归纳不确定性集合理论研究进展的基础上拓展其应用。方法历史分析法和文献考证。结果通过对Fuzzy集、Vague集和Rough集等研究,从不同的角度拓展了经典的集合理论,并对他们之间的关系作了深入的探讨。结论使得集合论的应用领域扩展到含糊的、不确定性问题上来。

Aim To introduce Fuzzy set; Vague set; Rough set and reveal their interrelationships. Methods And then based on the reseach development of inducing the uncertainty set theory, their applications are extended. Resuits The methods include historical analyses and texual researches. Conclusion The results are that classical set theories are extended from various angles through the study of Fuzzy set, Vague set and Rough set and further researches on their interrelationships are also explored. The conclusion ： the application of set theories are into vague and uncertainty problems.