Logic of prototypes and counterexamples: possibilities and limits
Thomas Vetterlein · Advances in intelligent systems research/Advances in Intelligent Systems Research · 2015
Fuzzy sets are a popular tool to model vague properties.It is, however, well-known that this model usually involves a good degree of arbitrariness.In this contribution we consider the possibility of standardising the construction of fuzzy sets at least with regard to the borderline cases.To this end, we identify a vague property with the sets of clearly positive cases and clearly negative cases and under the assumption that the universe of discourse is a metric space, we determine the fuzzy set by what can be described as a linear interpolation.Following this idea, we discuss a number of logic-based approaches to reasoning under vagueness.