Actuaries working in claims reserving are often faced, among others, with the following two tasks: the prediction of future outstanding loss liabilities, as well as the quantification of their risk. Within claims reserving there exist various methods in which vagueness and subjective judgement is often not considered. A formal approach is given e.g. by fuzzy set theory. Besides an overview of applications of fuzzy set theory in claims reserving the author presents three ways of how subjective assessment can be implemented in the chain-ladder as well as the Bornhuetter Ferguson method.