Fuzzy rating scales: Does internal consistency of a measurement scale benefit from coping with imprecision and individual differences in psychological rating?

•The use of fuzzy rating scales to capture imprecision and individual differences.•The extension of Cronbach?s alpha for fuzzy scale-based items.•Influence of the number of items while scarce influence of the fuzzy responses’ shape.•The comparison of standard and fuzzy scales through alpha.•The novel simulation process to mimic dependence between items in a construct.