On Quantified Linguistic Approximation
  Most fuzzy systems including fuzzy decision support and fuzzy control systems
provide out-puts in the form of fuzzy sets that represent the inferred
conclusions. Linguistic interpretation of such outputs often involves the use
of linguistic approximation that assigns a linguistic label to a fuzzy set
based on the predefined primary terms, linguistic modifiers and linguistic
connectives. More generally, linguistic approximation can be formalized in the
terms of the re-translation rules that correspond to the translation rules in
ex-plicitation (e.g. simple, modifier, composite, quantification and
qualification rules) in com-puting with words [Zadeh 1996]. However most
existing methods of linguistic approximation use the simple, modifier and
composite re-translation rules only. Although these methods can provide a
sufficient approximation of simple fuzzy sets the approximation of more complex
ones that are typical in many practical applications of fuzzy systems may be
less satisfactory. Therefore the question arises why not use in linguistic
ap-proximation also other re-translation rules corre-sponding to the
translation rules in explicitation to advantage. In particular linguistic
quantifica-tion may be desirable in situations where the conclusions
interpreted as quantified linguistic propositions can be more informative and
natu-ral. This paper presents some aspects of linguis-tic approximation in the
context of the re-translation rules and proposes an approach to linguistic
approximation with the use of quantifi-cation rules, i.e. quantified linguistic
approxima-tion. Two methods of the quantified linguistic approximation are
considered with the use of lin-guistic quantifiers based on the concepts of the
non-fuzzy and fuzzy cardinalities of fuzzy sets. A number of examples are
provided to illustrate the proposed approach.
