Database Reference
In-Depth Information
Lavency (1987). Their approach was quickly followed by Bosc & Pivert (1992c,1993), and then extended
and discussed in detail by Dubois & Prade (2002,2008) and in our papers (Matthé & De Tré, 2009;
Zadrożny, 2005; Zadrożny & Kacprzyk, 2006, 2007, 2009a; De Tré et al., 2009).
In the most general setting relevant for our considerations, bipolarity is understood as follows. The
user expressing his or her preferences concerning the data sought is assumed to consider both
positive
and
negative
aspects. Both may be considered more or less independently and may be aggregated (or
not) by the user in many different ways. Thus, our aim should be to provide the user with means making
expression of such bipolar preferences as convenient as possible.
Bipolarity may be modeled by using the two basic models (Grabisch, Greco & Pirlot, 2008):
bipolar
univariate
and
unipolar bivariate.
The former assumes one scale with three main levels of, respectively,
negative, neutral and positive evaluation, gradually changing from one end of the scale to another, giving
rise to some intermediate levels. The latter model of bipolarity assumes two independent scales which
separately account for positive and negative evaluation. In the first case the negative and positive as-
sessments are somehow combined by the user and only an aggregated overall assessment is expressed
as one number, usually from the [-1, 1] interval. Intuitively, the negative numbers express an overall
negative assessment, 0 expresses the neutral assessment and the positive numbers express an overall
positive assessment. In the case of the unipolar bivariate scale, the positive and negative assessments
are expressed separately on two unipolar scales, usually by two numbers from the [0,1].
Now, we will briefly discuss various aspects of the concept of bipolarity in the context of flexible
fuzzy queries because we think it is important to distinguish various interpretations of this term used
in the literature.
First, in the classic fuzzy approach a unipolar univariate scale is tacitly assumed as we have a degree
to which given attribute value is compatible with the meaning of a given linguistic term
l
and, thus, the
degree to which this value satisfies a query condition. There is no way to distinguish between “negative”
(“rejected”, “bad”) and “positive” (“accepted”, “good”) values.
The bipolarity may manifest itself
at the level of each attribute domain
or
at the level of the compre-
hensive evaluation
of the whole tuple. In the former case, the user may see particular elements of the
domain as “negative”, “positive” or “neutral”, to a degree. This classification should, of course, influence
the matching degree of a tuple having particular element of the domain as the value of the attribute under
consideration. In the latter case the user is expected to express some conditions, involving possibly many
attributes, which - when satisfied by a tuple - make it “negative” or “positive”.
In case of the unipolar bivariate model we can distinguish a special interpretation which is further
discussed in this paper. Namely, the negative and positive assessments are treated as corresponding to the
conditions which are
required
and
preferred
to be satisfied, respectively. Thus, the former condition has
to be satisfied necessarily and the latter only
if possible
. The negative assessment in this interpretation
is identified with the degree to which the required condition is
not
satisfied. For example, if a person
sought has to be young (the required condition), then its negative assessment corresponds to the degree
to which he or she is not young, i.e., to which it satisfies the negation of the required condition. The
preferred condition, on the other hand, characterizes those tuples (persons) which are really desired, with
an understanding that the violation of such a condition by a tuple does not necessarily cause its rejection.
The above special interpretation of bipolarity is in fact predominant in the literature. Lacroix and
Lavency (1987) first introduced a query comprising two categories of conditions: one which is manda-
tory (
C
) and another which expresses just mere preferences (desires) (
P
). The bipolarity of these condi-
tions becomes evident when one adopts the following interpretation. The former condition
C
expresses
