In this paper, limit theory of set-valued functions defined on an interval (for short, isv-functions) is preliminarily established. Firstly, the concept of isv-functions is introduced. Secondly, limits of isv-functions are proposed and their properties are obtained. Thirdly, point-wise continuity of isv-functions and continuous isv-functions are discussed. Finally, an application of this theory for rough sets is given.
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