n-维区间向量与n-维区间值函数

【作者】 赵新虎；

【导师】 王贵君；

【作者基本信息】 天津师范大学 ， 应用数学， 2011， 硕士

【摘要】 区间分析的出现几乎与模糊数学处于同一个时期,它以新颖的思想开拓了其发展途径和研究领域,其应用范围也已经涉及到许多方面。事实上.在模糊数学的理论研究中,许多地方可以应用区间分析方法来处理。因此.按照数学的思维方式与体系,如何将区间分析理论广泛应用到模糊数学领域是一项十分有意义的工作。第一部分：区间数和区间值函数。一方面,在区间数的一些基本运算和性质基础上,借助区间数距离讨论了区间数序列的收敛性,获得了类似实数列的一些性质。另一方面,以区间数理论为工具,针对区间值函数研究了及其极限及其运算问题,特别是对连续区间值函数进行了深入探讨,获得了关于连续区间值函数的最值性定理。第二部分：N-维区间向量与n-维区间值函数。首先,利用区间数给出了n-维区间向量的概念,讨论了n-维区间向量的运算及性质：其次.在n-维区间向量空间上,通过引入向量模定义了距离,并借助于该距离系统研究了n-维区间向量序列的一些收敛性质；最后,应用n-维区间向量模和距离刻画了n-维区间值函数的极限及其连续性问题,获得了类似于区间值函数的一些重要结论.这些结果对进一步研究多维模糊值函数及应用奠定了理论基础。更多还原

【Abstract】 The emergence of interval analysis and fuzzy mathematics is almost in the same period.They open up its development and research with innovative thinking of ways.What is more,its scope of application has also been involved in many aspects. In the study of Fuzzy mathematics, there are many places to deal with interval analysis. This is a very meaningful project to be extended to the field of fuzzy mathematics with the theory of interval analysis in accordance with the mathematical system and the way of thinkingThe first part is about the interval numbers and interval-valued functions. Firstly,with the distance between the interval numbers,we discussed the conver-gence of interval sequences in the natures of the interval numbers, then obtained some properties which are similar to real numbers. And we studied the limits and and the operational properties of interval-valued functions.For the continu-ous interval-valued functions, we researched his most valued theorem.The second part is about the n-dimensional interval vectors and n-dimensional interval-valued function.We used interval numbers for the definition of n-dimensi onal interval vectors, discussed the operational properties of n-dimensional inter-val vectors.Then in the space of n-dimensional interval vectors we defined the distance by way of the vector mode and researched systematically the conver-gence of n-dimensional interval sequences on the basis of the distance of the n-dimensional interval vectors.Finally,we characterized the limit and the conti-nuity of n-dimensional interval valued-function by vector mode and the distance and obtained some important results like interval valued-function.The results laid a theoretical foundation for further studying and applying of multi-dimensional fuzzy-valued functions.更多还原