A Flexible Approach to Matching User Preferences
with Records in Datasets based on the Conformance Measure
and Aggregation Functions
Miljan Vučetić
1
and Miroslav Hudec
2
1
Vlatacom Institute of High Technologies, 5 Milutina Milankovića Blvd, Belgrade, Serbia
2
Faculty of Economic Informatics, University of Economics in Bratislava, Dolnozemská cesta 1, Bratislava, Slovakia
Keywords: Similarity, Conformance Measure, Fuzzy Conjunction, Uni-norms, Geometric Mean, Quantified Fuzzy
Aggregation.
Abstract: Matching user preferences with content in datasets is an important task in building robust query engines.
However, this is still a challenging task, because the entities’ attributes are often expressed by various data
types including numerical, categorical, and fuzzy data. Moreover, the user’s preferences and data types for
particular attributes may not collide, i.e. the user explains his requirements in linguistic term(s), whereas the
respective attribute is recorded as a real number and vice versa. Further, the user may provide different
relevancies for atomic conditions, where usual one-directional reinforcement aggregation functions, e.g.
conjunction, are not suitable. In this paper, we propose a robust framework capable to manage user
requirements and match them with records in a dataset. The former is solved by conformance measure,
whereas for the latter the suitable aggregation functions have been suggested to cover particular aggregation
needs. Finally, we discuss benefits, drawbacks and outline further activities.
1 INTRODUCTION
When searching for suitable entities (customers,
products, territorial units, etc.) in a dataset, users
may have a variety of requirements in mind (desired
values of entities’ attributes), which the best matches
should meet. Users require that search process
provides them with sensible responses to their
requests (Snasel et al., 2007).
In a dataset, attributes’ values can be stored by a
variety of data types and may be heterogeneous, i.e.
values of one attribute may be stored for some
records as numeric, whereas for others as fuzzy or
categorical data. On the other hand, users can
explain their expectations linguistically or
numerically. Hence, user preferences and datasets
are a mixture of data types including numerical,
categorical, binary, and fuzzy data. Moreover, users’
preferences and the data types for particular
attributes may not collide. A user may explain that
the desired flat distance to the lake is very short or
short, whereas the distance attribute is recorded as a
real number greater than 0. In the opposite case, a
user may say that he/she expects the distance to the
public transport to be within 200 m, but in a dataset
the distance is expressed linguistically by one of the
following terms: very short walking distance, short
walking distance, medium walking distance, long
walking distance, beyond walking distance. This
makes application of fuzzy queries such as:
FQUERY (Kacprzyk and Zadrożny, 1995), FQL
(Wang et al., 2007), SQLf (Bosc and Pivert, 1995),
GLC (Hudec, 2009), FSQL (Urrutia et al., 2008),
PFSQL (Škrbić and Racković, 2009) and their
further extensions, hard. Therefore, the promising
option is applying conformance measures (Sözat and
Yazici, 2001), initially developed for calculating
fuzzy functional dependencies (Sachar, 1986). In
this paper, the definition of conformance is different
from the one presented in the mentioned studies and
is in the line with (Vucetic, 2013), which is based on
the fuzzy sets and proximity relation.
Further, the overall query condition may consist
of higher number of atomic ones (e.g. features of
products which should be met). It restricts query
answer to few records, but the possibility of the
empty answer problem (Bosc et al., 2008) may
appear as well. The quantified queries of the
168
Vu
ˇ
ceti
´
c, M. and Hudec, M.
A Flexible Approach to Matching User Preferences with Records in Datasets based on the Conformance Measure and Aggregation Functions.
DOI: 10.5220/0006925801680175
In Proceedings of the 10th International Joint Conference on Computational Intelligence (IJCCI 2018), pages 168-175
ISBN: 978-989-758-327-8
Copyright © 2018 by SCITEPRESS – Science and Technology Publications, Lda. All rights reserved

structure: most of atomic conditions should be met
(Kacprzyk and Ziółkowski 1986), or relaxing atomic
conditions (Bosc et al., 2009) are the possible
solutions. The former does not divide atomic
conditions into hard (must be at least partially met)
and soft (it is nice if they are met as well), i.e. a
record is a solution even if it does not meet one of
the atomic conditions, regardless the importance of
this condition. Hence, the possible solutions are
quantifying hard and soft constraints suggested by
Kacprzyk and Zadrożny (2013) and Hudec (2017).
Relaxing query condition is a complex task of
relaxing the most suitable atomic predicates by
keeping the semantic meaning as close as possible to
the initial query (Bosc et al., 2009). In addition,
users can express preferences among atomic
conditions by various ways: equal preferences,
weights, constraints and wishes, etc. When all
atomic conditions should be met at least partially,
the often used and connective or conjunction
expressed by t-norms copes with the
non-compensatory effect and downward
reinforcement (Beliakov et al., 2007).
This study examines benefits of calculating
conformances initially developed in (Vucetic et al.,
2013) and recently applied in recommending less-
frequently purchased products (Vučetic and Hudec,
2018) to reveal how user’s requirements and items
(records) in the dataset are conforming with the
considered attributes. The second part of this study
considers suitable aggregations of atomic conditions
in order to cover the most expected preferences
among attributes raised by users.
2 CONFORMANCE MEASURE
The fuzzy conformance-based approach is suitable
for calculating similarity measures among attributes’
values and matching complex user requirements
with records in a dataset when mixed-type attributes
are considered.
The conformance measure is used to compare
expected and existing values of particular attributes.
In this sense, the value of conformance in the
interval [0, 1] is reasonable for observing how the
user’s requirements and items in the dataset match.
Therefore, amongst many methods, this approach is
more natural for comparing given crisp, categorical
and fuzzy data that appear in user preferences and
attributes’ values. Although data may be
heterogeneous, we are able to straightforwardly
measure the similarity between user requirements
and item features by (Vučetić, 2013):
C(X
i
[t
u
,t
j
]) = min( μ
tu
(X
i
), μ
tj
(X
i
), s(t
u
(X
i
), t
j
(X
i
)))
(1)
where C is a fuzzy conformance of attribute X
i
defined on the domain D
i
between user requirement
t
u
and record t
j
in a dataset, s is a proximity relation
and
μ
tu
(X
i
) and μ
tj
(X
i
) are membership degrees of
user preferred value and value in a dataset,
respectively.
When we analyse fuzzy data, it is necessary to
answer how fuzzy value B belongs to the fuzzy set A
(e.g. price about 1 000 belongs to the fuzzy set
medium price). This is realized by the possibility
measure defined as (Galindo, 2008; Zadeh, 1978):
( , ) sup [ ( ( ), ( ))]
xX
Poss B A t A x B x
∈
=
(2)
where X is a universe of discourse and t is a t-norm.
In practice, minimum t-norm is used. This equation
is used to get membership degree when fuzzy data
appears in user requirements and item features in a
dataset.
In order to match user requirements with items in
a dataset, the first step is fuzzification of attributes
domains and definition of proximity relations. For
instance, the attribute walking distance is fuzzified
into several fuzzy sets, as shown in Figure 1.
The fuzzy conformance relies on proximity
relations for each attribute domain. These relations
are reflexive and symmetric and do not meet the
constraint of max-min transitivity as similarity
relation does (Shenoi and Melton, 1999).
Proximity relation is defined on the scalar
attribute domain and we integrate it under fuzzified
domain for numerical attributes. Specifically, by
employing fuzzy sets for domain partitions, it is
possible to describe similarities between mixed data
types. Algorithms (Vučetić and Hudec, 2018; Tung
et al., 2006; De Pessemier et al., 2014) calculate the
intensity of compatibility between desired value and
values of each record (item) in a dataset.
The distance (to the lake, for example) is in our
case fuzzified as very short walking distance, short
walking distance, medium walking distance, long
walking distance, beyond walking distance as
illustrated in Figure 1. In this way we work with
numerical data and linguistic terms as is shown in
examples below. The same holds for the other
attributes. For simplicity reasons, these linguistic
terms are mathematically formalized by liner
membership functions. The proximity relation
among these linguistic terms is shown in Table 1.
A Flexible Approach to Matching User Preferences with Records in Datasets based on the Conformance Measure and Aggregation Functions
169

Figure 1: An example of fuzzified attribute walking distance.
Table 1: Proximity relation over walking distance domain,
where wd stands for walking distance.
S
wd
very
short
wd
short
wd
medium
wd
long
wd
beyond
wd
v.sh. wd 1 0.90 0.50 0.10 0
short wd 1 0.80 0.25 0
med. wd 1 0.85 0.45
long wd 1 0.65
beyon wd 1
Let us observe the following examples. The user
could start with the preferred walking distance
(attribute A
1
) t
u
(Walk_Dist) of less than 200 m.
Membership degree to the fuzzy set very short
walking distance is
μ
tu
(Walk_Dist) = 1 using Eq. (2).
For each pair of user requirement and item in the
dataset, we use Eq. (1).
In the case of t
1
(Walk_Dist) = 215 m, the
membership degree to the fuzzy set very short
walking distance is
μ
t1
(Walk_Dist) = 0.85 and s(very
short, very short) = 1, when parameters a = 200 and
b = 300 in Figure 1:
C(Walk_Dist[t
u
, t
1
]) = min( μ
tu
(Walk_Dist),
μ
t1
(Walk_Dist), s(t
u
(Walk_Dist), t
1
(Walk_Dist)))
= min(1, 0.85, 1) = 0.85
The conformance of t
u
and t
2
(Walk_Dist) =
around 670 m (membership degree to the fuzzy set
medium walking distance is
μ
t2
(Walk_Dist) = 0.70
using Eq.(2) where c = 600, d = 700, Figure 1) is
given as:
C(Walk_Dist[t
u
, t
2
]) = min( μ
tu
(Walk_Dist),
μ
t2
(Walk_Dist), s(t
u
(Walk_Dist), t
2
(Walk_Dist)))
= min(1, 0.70, 0.50) = 0.50
The conformance of t
u
and t
3
(Walk_Dist), where
t
3
contains linguistic term long wd is by (1):
C(Walk_Dist[t
u
, t
3
]) = min( μ
tu
(Walk_Dist),
μ
t3
(Walk_Dist), s(t
u
(Walk_Dist), t
3
(Walk_Dist)))
= min(1, 1, 0.10) = 0.10
It should be noted that conformance may be
zero. For example, C(Walk_Dist[t
u
, t
4
]) between t
u
and t
4
(Walk_Dist) = 2130 m (membership degree to
the fuzzy set beyond walking distance is
μ
t4
(Walk_Dist) = 1,when h = 2100 m in Figure 1) for
s(very short, beyond) = 0 from Table 1 is calculated
as follows:
C(Walk_Dist[t
u
, t
4
]) = min( μ
tu
(Walk_Dist),
μ
t3
(Walk_Dist), s(t
u
(Walk_Dist), t
4
(Walk_Dist)))
= min(1, 1, 0) = 0
Obviously, the conformance of t
u
and t
5
, where t
5
contains numerical value of 195 m is 1. These
conformances are shown in Table 2, for attribute A
1
.
Similarly, we calculate conformances for the
other attributes. For instance, attribute A
2
is energy
consumption expressed by linguistic terms. The user
may express preferred value as a subset {very low,
low}, whereas stored data may be expressed by one
term when the observation is clear, or by two terms
when expert has doubts between, e.g. low and
medium.
The conformance on binary data usually gets
value 0 or 1, when the proximity between Yes and
No is 0. Theoretically, the proximity can be greater
than 0, when these two opposite cases are not fully
exclusive for users. For instance, in Table 2 attribute
A
4
expresses presence of the elevator in the block of
flats. The rest of attributes may be any attribute, e.g.
size of flat, storey and aggregated opinion about
location on social networks.
Our notion of fuzzy conformance is related to
the calculated degree of similarity between user
requirements and items in a dataset per particular
attribute.
IJCCI 2018 - 10th International Joint Conference on Computational Intelligence
170

Table 2: Fuzzy conformances of attributes A
1
to A
7
between user preferences expressed by vector of ideal values t
u
and
records t
1
to t
5
.
record C(A
1
[t
u
, t
j
]) C(A
2
[t
u
, t
j
]) C(A
3
[t
u
, t
j
]) C(A
4
[t
u
, t
j
]) C(A
5
[t
u
, t
j
]) C(A
6
[t
u
, t
j
]) C(A
7
[t
u
, t
j
])
t
1
0.85 0.85 0.85 1.00 0.85 0.85 0.85
t
2
0.50 0.25 0.26 1.00 0.29 0.24 0.27
t
3
0.10 0.65 0.46 1.00 0.41 0.88 0.44
t
4
0.00 0.95 0.88 1.00 1.00 0.90 0.85
t
5
1.00 0.25 0.65 0.00 0.25 0.00 0.35
Table 3: Aggregation by t-norms, uni-norm and geometric mean.
record C(A
1
) C(A
2
) C(A
3
) C(A
4
) C(A
5
) C(A
6
) C(A
7
)
min t-
norm
(4)
product
t-norm
(5)
uninorm
(6)
geomet-
ric mean
(7)
t
1
0.85 0.85 0.85 1.00 0.85 0.85 0.85 0.85 0.3771 1.00 0.8699
t
2
0.50 0.25 0.26 1.00 0.29 0.24 0.27 0.24 0.0006 1.00 0.3474
t
3
0.10 0.65 0.46 1.00 0.41 0.88 0.44 0.10 0.0047 1.00 0.4656
t
4
0.00 0.95 0.88 1.00 1.00 0.90 0.85 0.00 0.0000 0.00 0.0000
t
5
1.00 0.25 0.65 0.00 0.25 0.00 0.35 0.00 0.0000 0.00 0.0000
In the next step, each fuzzy conformance is
combined with the aggregation operator to meet user
preferences in accordance with his expectations
regarding all of the attributes.
The simplest case for finding the best matching
record is when a record/item is dominant by all
atomic conditions, or is equal to all but one atomic
condition and is better than the last one, i.e.
11 1 1
() () () ()
( ) ( ) , 1 ,
j
kjk mjmk
mj mk
t t Vt Vt V t V t
Vt Vt jk nj k
−−
⇔≥∧∧ ≥
∧> = ≠


(4)
where for clarity conformances are expressed as
([,]) ()
iu j i j
CAt t Vt=
.
However, in reality, a record can be more
suitable by one and less suitable by another atomic
condition or conformance. This case is illustrated in
Table 2 for conformance of seven attributes between
user preferences t
u
and records t
1
to t
5
in a dataset.
The next section is focused on the aggregation of
conformances in order to cope with different
characters of user preferences.
3 AGGREGATION OF ATOMIC
CONDITIONS EXPRESSED BY
CONFORMANCE MEASURES
This section examines several most expected cases
of aggregation of conformances among attributes
covering different kinds of preferences which might
be raised by users.
3.1 Conjunction of Equally Important
Atomic Conditions Expressed by
Conformance
The simplest case is when all conditions are equally
important and should be at least partially met. This
naturally leads to the aggregation by conjunction,
expressed through t-norms. On the other hand, t-
norms lack compensation effect, i.e. minimum t-
norm (Beliakov et al., 2007) adjusted for
conformances (1) for record t
j
:


_

=min
,…,
(

[

,

])
(4)
(where n is the number of atomic conditions), or
have property of downward reinforcement, i.e.
product t-norm (Beliakov et al., 2007), also adjusted
to conformances (1):

_
=(

[

,

])


(5)
More precisely, except the minimum t-norm all
other t-norms have the property of downward
reinforcement.
This problem is illustrated in Table 3 on the data
from Table 2. When six attributes are conforming
with value of 0.85 each (record t
1
), and one is
conforming with value of 1 (neutral element) the
overall similarity to the user requirements is 0.3771
calculated by product t-norm (5) (downward
reinforcement).
A Flexible Approach to Matching User Preferences with Records in Datasets based on the Conformance Measure and Aggregation Functions
171

T-norms map result into the unit interval, i.e.
[0, 1]
n
→ [0, 1], where 1 is the ideal case. It might
lead user to conclude that the record t
1
is not very
similar to the desired one by (5); that is, it is far from
the ideal value. The solution based on the minimum
t-norm (4) reveals the problem of non-compensatory
effect, ranking t
2
higher than t
3
, even though t
3
is
significantly more suitable in all but one
conformance and worse in attribute A
1
, i.e. values
higher than the minimum are not considered.
The disjunction is not the option, because it is
not restrictive (value 1 is annihilator), and
t-conorms, which model disjunction, also have
one-directional, in this case the upward
reinforcement property (Beliakov et al., 2007).
Therefore, an alternative may be uni-norms.
They meet the property of full reinforcement
(Beliakov et al., 2007) punishing low values (as
conjunction does) and emphasizing high values (as
disjunction does), in our case values of
conformances. The 3-
∏ function (Yager and
Rybalov, 1996) is adjusted to calculate conformance
(1) for record tj as:

_
=
∏
(

[

,

])


∏
(

[

,

])


+
∏
(1−



,

)


(6)
The product in numerator (6) ensures that only
the records (items) that at least partially meet all
conditions are considered, i.e. value 0 is annihilator.
The consequence of being mixed aggregation
functions is that value 1 is also annihilator. The uni-
norm has desired behaviour when matching degrees
of conformances are in the open interval (0, 1).
Applying (6) on data in Table 3, has shown that t
1
–
t
4
fully meet the condition whereas t
4
and t
5
are fully
rejected. Record t
4
has conformance equal to 0 for
attribute A
1
and therefore is excluded by both:
t-norms and uni-norms.
Another options are averaging aggregation
functions, but only the borderline case with
conjunction functions, to meet the requirement that
all atomic conformances should be at least partially
met, is suitable. Thus, the solution is geometric
mean:

_
=

(

[

,

])


/
(7)
Applying (7) on data in Table 3 (last column),
has shown that t
1
is emphasized, but not as by uni-
norm (6), t
3
got better evaluation than t
2
as is
expected due to better behaviour in majority of
conformances. Records t
4
and t
5
have got
conformances equal to 0 for one or more attributes
and therefore are excluded by all functions: t-norms,
uni-norms and geometric mean.
Although, t-norms are widely used in computing
matching degrees for conjunction, the benefit of
geometric mean and in the restricted cases of uni-
norms should not be neglected, especially when a
high number of atomic conformances is considered.
In the case of a small number of atomic conditions,
t-norms are suitable.
3.2 Quantified Condition of Atomic
Conformances
In the aggregations by t-norms, uni-norms and
geometric mean the record is excluded when all but
one condition are met. It especially holds when the
user provides higher number of atomic conditions.
However, not all of them must always be met. In this
case, we can consider quantified query condition:
most of atomic conditions should be met (Kacprzyk
and Ziółkowski, 1986) or, in our case, most of
conformances should be greater than 0. For this
purpose we adjusted equation from fuzzy quantified
queries (Hudec, 2017) to conformances in the
following way:
1
1
() ( ([,]))
n
jQ iuj
i
vt C A t t
n
μ
=
=

(8)
where v is the validity or matching degree for item t
j
to quantified condition, n is the number of
conformances and µ
Q
is the function of relative
quantifier most of in the sense of Zadeh (1983)
which can be re-formalized as:
00.5
0.5
( ) (0.5, 0.9)
0.4
10.9
Q
y
y
yy
y
μ
≤


−

=∈


≥


(9)
Obviously, the ideal record is one with
conformance values equal to 1 for all attributes,
regardless the applied aggregation.
Regarding Tables 2 and 3, the best match is t
1
with validity of 0.929, followed by t
4
with validity
0.743. Record t
3
has low validity, more precisely
0.157, and the validities of records t
2
and t
5
are zero.
Although, record t
2
met all atomic preferences, these
low values are reflected in the proportion. On the
other hand record t
4
failed to meet one conformance,
IJCCI 2018 - 10th International Joint Conference on Computational Intelligence
172

but significantly met other ones. This aggregation is
suitable when all conditions are considered as soft
ones, i.e. it is not imperative that a particular atomic
condition should be met, but majority of them.
We should be careful, because this approach is
not suitable when several conformances should be
imperatively greater than zero. For instance, when
one of the considered attributes is price, and the user
cannot afford the product that is beyond budget even
if all other features are excellently met. The next
subsection examines this case.
3.3 Merging Quantified Query
Conditions with Conjunction and
Other Aggregations
We should be careful with quantified conditions
because some of the atomic conditions may be hard
constraints like price. If price is beyond the limit, it
is irrelevant whether other conditions are met. Such
conditions we call hard ones, which we should
manage in quantified queries separately. The
suitable solution is aggregating hard conditions with
the soft ones, managed by quantified condition (8),
by conjunction:


=(∧






,

)∧

(
1





,




)
(10)
where p is the number of hard conditions and q is the
number of soft conditions.
In Section 3.2, the second option is record t
4
form Table 3. However, if the conformance of
attribute A
1
is a hard condition, e.g. instead walking
distance it represents price, this record is irrelevant
and therefore the aggregated value should be 0. The
aggregation by (10) provides the expected results
shown in Table 4. The results differ in comparison
to Table 3 and Section 3.2 because the nature of
preferences is changed.
Table 4: Aggregation of hard conditions and quantified
condition by (10).
record
hard
condition
quantified
condition
solution by
min t-norm
in (10)
t
1
0.85 0.875 0.85
t
2
0.50 0.00 0.00
t
3
0.10 0.350 0.10
t
4
0.00 1.000 0.00
t
5
1.00 0.000 0.00
For conjunction in (10), we can use any t-norm,
but we should be aware of the strengths and
weaknesses discussed in Section 3.1. We can also
apply uni-norm (6) or geometric mean (7) in (10)
instead of t-norms.
3.4 Discussion
The inspiration for this work were problems with
buying flats, where higher number of attributes is
considered. Further, collected data may be mixed
data types, i.e. numerical, categorical or fuzzy for
the same attribute. In addition, user may explain
large scale of preferences among attributes.
Moreover, we cannot fully rely on recommender
systems for less-frequently bought products, because
the history of similar customers is weak (Vučetić
and Hudec, 2018).
Aggregation operators should be able to cover
variety of preferences among atomic conditions, or
in our case conformances. The conformance
measure reveals how user requirements and items
(records) in the dataset are conforming to the
considered attributes.
When small number of atomic conditions is
included and all should be at least partially met, the
options are t-norms, which formalize conjunction in
the fuzzy environment.
On the other hand, when higher number of
conformances is included, where all of them should
be at least partially, the best matches emphasized
(upward reinforcement) and the weak matches
punished (downward reinforcement), the solution
seems to be reached by uni-norm which have
property of full reinforcement, e.g. 3-Π function (6).
The product in nominator eliminates items which
fail to meet at least one conformance. But, when
only one conformance is fully met, item ideally
meets requirements regardless other conformances.
The aggregation function, which meets the
following requirements: 0 as annihilator,
compensation effect without downward
reinforcement and value 1 is the neutral element not
the annihilator, is geometric mean. This function is
the borderline case between conjunctive and
averaging aggregation functions.
Further, when a user provides a larger number of
atomic conditions, where not all of them must be
met, the aggregations by t-norms, uni-norms and
geometric mean are not suitable. The solution is
quantified aggregation of the structure most of
conformances should be (significantly) met.
Finally, when several conformances must be met
and at least majority of others, the solution is
aggregation between hard conditions (conformances
which must be at least partially met) and soft
A Flexible Approach to Matching User Preferences with Records in Datasets based on the Conformance Measure and Aggregation Functions
173

conditions (it is beneficial if majority of these
conformances are met, i.e. quantified aggregation)
by t-norms or geometric mean.
An illustrative example was used to demonstrate
various options of conformances among mixed data
types and aggregations. Anyway, this approach is a
universal framework for working with the real-life
data.
4 CONCLUDING REMARKS
In queries, users may be interested in higher number
of atomic conditions expressed through preferred
values of respective attributes. Fuzzy conformance
has been proven to be a very useful approach to
measure how user preferences conform to the values
stored in datasets. Our work addresses the problem
of matching data that contain numerical, categorical,
binary and fuzzy data in attributes. The goal is
building a framework that automatically handles
these mixed data types and different characterization
of user preferences. Fuzzy conformance is also the
object of intense research activities in other fields
such as discovering fuzzy functional dependencies,
product recommendation techniques, data fusion in
fuzzy relations etc.
Users may also express different natures of
preferences among attributes in queries. Although
t-norms are widely used in computing matching
degrees of atomic conditions, the benefit of
geometric mean and possibilities of uni-norms
should not be neglected when higher number of
atomic conformances is considered due to
non-compensatory effect or downward
reinforcement property of t-norms. The geometric
mean is a suitable solution, because the product of
atomic conformances ensures that only the records
that at least partially meet all conditions are
considered.
Further, higher number of atomic condition may
lead to the problem known as empty answer
problem. The suggested solution is a quantified
condition of the structure most of atomic
conformances should be met. But, when several
atomic conditions are hard, (e.g. if price is beyond
the budget limits, record is irrelevant regardless it
met other requirements ideally), the solution is
connective expressed by t-norms, uni-norms or
geometric mean between hard conditions and soft
conditions in a quantified query.
This study may help software developers to
include further flexibility into the data retrieval tasks
for data users, when the users consider higher
number of atomic features, mixed data types and
large scale of possible aggregations among atomic
conformances. The overall matching degree in the
unit interval clearly indicates how far the considered
records to the ideal one are.
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