The representation of linguistic hedges using fuzzy relational calculus

Traditionally in fuzzy set theoretical frameworks linguistic hedges are modelled by technical operators lacking inherent meaning. In this paper we elaborate on a recently developed representation of modified linguistic expressions that takes into account mutual relationships between objects of the universe. Formally this is accomplished by modelling hedges by means of taking images under fuzzy relations: for ordering-based hedges orderings and strict orderings are used, while for weakening and intensifying hedges we propose to use fuzzy relations modelling approximate equality. Since fuzzy T-equivalence relations prove to be unsuitable for this purpose, resemblance relations are chosen instead. The resulting framework not only allows for a unified approach to the modelling of hedges but also endows them with an inherent semantics, thereby overcoming important shortcomings of the traditional approaches, as we will illustrate by means of several examples in numerical as well as non-numerical universes.