2023 International Conference on the Cooperation and Integration of Industry, Education, Research and Application (Chongqing)
New Generation of Information Technology Working Conference

The 9th International Conference on Fuzzy Systems and Data Mining (FSDM 2023)

Abstract: For a convex set Y in the the n-dimensional Euclidean space Rⁿ, let K(Y) be the set of all fuzzy numbers whose supports are in Y. In K(Y), we can define some natural metrics, such as, the endograph metric D, the sendograph metric D' and the L_p metrics for 1≦p≦+∞, among others. In this talk, the topological structures of the spaces K(Y) with the above metrics will be given. More precisely, (1) (K(Y),D) and (K(Y),L_p) are homeomorphic for 1≦p<+∞. They are homeomorphic to the Hilbert cube Q if and only if Y is compact and to the pseudo-boundary of Q if and only if Y is locally compact non-compact. (2) (K(Y),D’) is homeomorphic to the Hilbert space l² if and only if Y is topologically complete. (3) (K(Y),L+∞) is homeomorphic to the Hilbert space l²(c) with the weight c if and only if Y is topologically complete.

Biography: Prof. Zhongqiang Yang was a doctoral supervisor at Department of Mathematics, Shantou University, China. At present, he is a professor in Minnan Normal University, China. He is mainly engaged in the research of topology and fuzzy mathematics, also, applications of topology to probability theory, topological dynamical systems, fuzzy mathematics and measure spaces. He has published more than 90 papers in high-level journals at home and abroad such as Fuzzy Sets and Systems, Science in China Ser. A Mathematics, Proc. Amer, Math. Soc. , Fund. Math., Topology Appl. and Houston J. Math. He has been funded by the National Natural Science Foundation for many times. Shantou University and Minnan Normal University are in leading positions in the field of infinite topology research in China.