A new definition of independence of uncertain sets

Uncertain sets are an effective tool to describe unsharp concepts like “young”, “tall” and “most”. As a key concept in uncertain set theory, the independence was first defined in the paper (Liu in Fuzzy Optim Decis Mak 11(4):387–410, 2012b). However, the definition is somewhat weak to deal with uncertain sets completely. In order to overcome this disadvantage, this paper presents a stronger definition of independence of uncertain sets and discusses its mathematical properties.