Database Reference
In-Depth Information
as, e.g.,
“
Most of recently hired employees are young
”
(23)
with “
T
(
most
of
recently hired
employees are
young
)=0.7”. The truth
T
may be meant in a more general
sense, e.g. as validity or, even more generally, as some quality or goodness of a linguistic summary.
The quantity in agreement,
Q
, is an indication of the extent to which the data satisfy the summary,
and two types of a linguistic quantity in agreement can be used:
•
absolute as, e.g., “about 5”, “more or less 100”, “several”, and
•
relative as, e.g., “a few”, “more or less a half”, “most”, “almost all”etc.
Notice that the above linguistic expressions are again the fuzzy linguistic quantifiers use of which we
advocate in the framework of fuzzy flexible querying. Thus, they may be modeled and processed using
Zadeh's (1983) approach and this way we obtain the truth
T
of a linguistic summary.
The basic validity criterion, i.e. the truth of a linguistically quantified statement given by (13) and
(14), is certainly the most natural and important but it does not grasp all aspects of a linguistic summary,
and hence some other criteria have been proposed, notably by Kacprzyk & Yager (2001), and Kacprzyk,
Yager & Zadrożny (2000). These include the degrees of imprecision, covering, appropriateness, the
length of a summary, etc. (cf. Kacprzyk & Zadrożny, 2010).
The problem is to find a best summary, i.e. with the highest value of some weighted average of the
satisfactions of the criteria assumed. One can clearly notice that a fully automatic determination of a
best linguistic summary may be infeasible in practice due to a high number of possible summaries ob-
tained via a combination of all possible linguistic quantifiers, summarizers and qualifiers. In (Kacprzyk
& Zadrożny, 2001a) an
interactive approach
was proposed with a
user assistance
in the selection of
summarizers, qualifiers and linguistic quantifiers. Basically, given a set of data
D
, we can hypothetize
any appropriate summarizer
S
, qualifier
R
and any quantity in agreement
Q
, and the assumed measure
of truth will indicate the quality of the summary.
In our interactive approach it is assumed that such hypothetic summaries are proposed by the user
via a flexible fuzzy querying interface, such as provided by FQUERY for Access. It may be easily no-
ticed that components of linguistic summaries are also components of fuzzy queries, as implemented in
FQUERY for Access. In particular, atomic conditions with fuzzy values are perfect simple summarizers
and qualifiers which may be further combined to obtain more sophisticated summaries. Linguistic quanti-
fiers are used in fuzzy queries to aggregate partial matching degrees but exactly the same computations
are required in order to obtain the truth of a linguistic summary. Therefore, the derivation of a linguistic
summary may proceed in an interactive (user assisted) way as follows:
•
the user formulates a set of linguistic summaries of interest (relevance) using the fuzzy querying
add interface,
•
the system retrieves records from the database and calculates the validity of each summary ad-
opted, and
•
a best (most appropriate) linguistic summary is chosen.
