A Fuzzy-Set-Theoretic Interpretation of Linguistic Hedges

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Abstract
A basic idea suggested in this paper is that a linguistic hedge such as very, more or less, much, essentially. slightly, etc. may be viewed as an operator which acts on the fuzzy set representing the meaning of its operand. For example, in the case of the composite term very tall man, the operator very acts on the fuzzy meaning of the term tall man. To represent a hedge as an operator, it is convenient to define several elementary operations on fuzzy sets from which more complicated operations may be built up by combination or composition. In this way, an approximate representation for a hedge can be expressed in terms of such operations as complementation, intersection, concentration, dilation, contrast intensification, fuzzification, accentuation, etc. Two categories of hedges are considered. In the case of hedges of Type I, e.g., very, much, more or less, slightly, etc., the hedge can be approximated by an operator acting on a single fuzzy set. In the case of hedges of Type II, e.g., technically, essentially, practically, etc., the effect of the hedge is more complicated, requiring a description of the manner in which the components of its operand are modified. If, in addition, the characterization of a hedge requires a consideration of a metric or proximity relation in the space of its operand then the hedge is said to be of Type IP or IIP depending on whether it falls into category I or II. The approach is illustrated by constructing operator representations for several relatively simple hedges such as very, more or less, much, slightly, essentially, etc. More complicated hedges whose effect is strongly context-dependent, require the use of a fuzzy-algorithmic mode of characterization which is more qualitative in nature than the approach described in the present paper.

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