对模糊集、Vague集和C*-模糊集的比较研究

模糊集、Vague集和C*-模糊集(新模糊集)都是对经典集合论的扩展,同时又是模糊集合论分支的发展成果。为完善模糊理论体系并将其有效应用,在介绍了三种集合的概念的基础上,分析了它们之间的区别和内在联系并参考与概率论统一定义的C*-模糊集合框架,提出了新Vague关系,使得在处理不确定问题的领域中有了完备的理论基础。最后对三个集合的发展和应用作了一些探讨性研究。

Comparative Study on Fuzzy Sets,Vague Sets and C*- Fuzzy Sets

Fuzzy set,Vague set and C*-fuzzy set(new fuzzy set) are extension of classical set theory.They are also results of fuzzy set theory development.For effective use of fuzzy theory and perfecting the theory system,difference and relationship between the three sets were discussed in detail on the basis of concepts from the three sets.After reference to the C*-fuzzy set framework uniformly defined in probability theory,a new Vague relation was proposed.The complete theoretical foundation was established for dealing with problems of uncertainty.Finally development and application of the three sets were discussed.