摘要
本文从数学的几次重大开拓出发,讨论了可拓集合产生的实际背景及其与经典集合、模糊集合的关系,进而从哲学基础与数学体系上论述了可拓域通过映射、变换可以化不相容问题为相容的理论根据,论证了可拓集合非空,奠定了客观世界中确实存在既是又非事物的数学基础.作者认为:可拓集合论与物元分析方法是解决客观世界中普遍存在的不相容问题的又一有力工具,这一工具的建立,无疑将会使数学在描述客观事物方面更加接近于实际.最后指出,可拓集合论的发展,必将导致可拓数学这一崭新分支的建立.
Starting with several important extensions, this paper discusses the actual background in which extension set has been developed the relationships between extension set and classical set or between extension set and fuzzy set. The paper further deals with the theoretical basis on which extension field can change inconsistent problems into the consistent through mapping or transformation. It also proves the nonempty of extension set, and thereforeit settles a mathematical foundation of objects both right and wrong which certainly exist in the object world. The author considers that both Theory of Extension Set and Method of Matter Elements Analysis are the powerful tools, which can solve the inconsistent problems existing universally in objective world. The establishment of these useful tools can doubtless make mathematics much closer to objective reality. This paper finally points out that the development of extension set will certainly result in the establishment of extension mathematics——a new branch in mathematics.
关键词
可拓集合
模糊集合
经典集合
extension set
fuzzy set
classical set
dependent function
pierabership function
characteristic function
