\(\mathbb{T}_ S\)-tribes and \(\mathbb{T}_ S\)-measures (Q1919603)

The paper deals with Frank's \(\mathbb{T}_s\)-norms, where \(s\in (0, \infty)\). The main result states that a family of fuzzy sets is a \(\mathbb{T}\)-tribe for each measurable \(\mathbb{T}\)-norm \(\mathbb{T}\) if and only if it is a \(\mathbb{T}_s\)-tribe for some \(s\in (0, \infty)\). A second important result states that each \(\mathbb{T}_s\)-measure \((s\in (0, \infty])\) defined on a \(\mathbb{T}_s\)-tribe is a generated measure.