基于宽度与期望值的区间值映射的若干性质

Some Properties of Interval-valued Mapping Based on the Width and Expectation

利用区间数的宽度和期望值讨论区间值映射的一些性质.首先给出了在基于宽度和期望值的序关系下的区间数集的有界及确界概念,并证明了有界区间数集必有确界;其次给出了区间值映射的EW-极限及EW-连续性概念,并建立了一些相关性质;然后讨论了区间值映射的EW-可微性问题,给出EW-导数及偏导数的概念,并讨论了EW-可导与H-可导之间的关系,证明了H-可导一定EW-可导.并举例说明了反之不一定成立.

In this paper,we discuss some properties of interval-valued mappings by the width and expectation of interval number.Firstly,we provide the concepts that interval number set have bound,supremum and infimum on the partial ordering relation of width and expectation and prove that bounded interval number set must have supremum and infimum.Secondly,we give the concepts of EW-limit and EW-continuity of interval-valued mapping and establish some related properties.Then we discuss the EW-differentiability of interval-valued mapping give the concepts of EW-derivative and EW-partial derivative,and discuss the relationship between EW-differentiability and H-differentiability.We prove that H-differentiable must be EW-differentiable and the reverse is not true.