An embedding theorem for fuzzy numbers on Banach spaces and its applications

Authors:
Jianrong Wu
Affiliations:
School of Power Engineering, Nanjing University of Science and Technology, Nanjing, People's Republic of China and Department of Mathematics, Suzhou Institute of Urban Construction and Environment ...
Venue:
Fuzzy Sets and Systems
Year:
2002

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Abstract

In this work, we give an embedding theorem for fuzzy number space N(X) on a Banach space X. As its applications, we show that some measurability concepts for fuzzy number valued mappings are equivalent, which partially solves an open problem given by Butnariu (Fuzzy Sets and Systems 31 (1989) 77). Additionally, we generalize some convergence theorems and Lusin Theorem to fuzzy random variables.