Affiliations: [a] School of Mathematics and Statistics, Key Laboratory of Hunan Province for Statistical Learning and Intelligent Computation, Hunan University of Technology and Business, Changsha, Hunan, P.R. China | [b] Key Laboratory of Complex System Optimization and Big Data Processing in Department of Guangxi Education, Yulin Normal University, Yulin, Guangxi, P.R. China
Abstract: 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.
Keywords: isv-function, limit, continuity, rough set
