N-dimensional Interval Vectors With N-dimensional Interval-valued Function

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.