A New Generation of the Fuzzy-set-theoretical Representation of Modified Linguistic Terms

Fuzzy set theory provides a framework in which natural language expressions can be modelled mathematically, thereby even taking the vagueness of linguistic terms into account. In fuzzy systems a linguistic term (e.g. fast) is represented by a fuzzy set, while a linguistic modifier (e.g. very) is modelled by an operator (also known as hedge) transforming a fuzzy set into another. In the paper first we give a short overview of the traditional fuzzy set theoretical approaches to this problem. We point out that these “hedges of the first generation” are in general technical tools without meaning of their own, which explains their most important shortcomings. To overcome this, we present two new approaches in which the representation of linguistic modifiers is endowed with an inherent semantics (“hedges of the second generation”): the framework of fuzzy modifiers based on fuzzy relations (recently developed by us) and the so-called horizon approach (an extension of the research initiated by Novák).