Silvia Calegari and Davide Ciucci
Dipartimento di Informatica, Sistemistica e Comunicazione,
a degli Studi di Milano Bicocca,
via Bicocca degli Arcimboldi 8,
20126 Milano, Italy
Concept modifiers, fuzzy logics, fuzzy ontologies, membership modifiers, KAON, ontology editor.
Ontologies have proved to be very useful in sharing concepts across applications in an unambiguous way.
Nowadays, in ontology-based applications information is often vague and imprecise. This is a well-known
problem especially for semantics-based applications, such as e-commerce, knowledge management, web por-
tals, etc. In computer-aided reasoning, the predominant paradigm to manage vague knowledge is fuzzy set
theory. This paper presents an enrichment of classical computational ontologies with fuzzy logic to create
fuzzy ontologies. So, it is a step towards facing the nuances of natural languages with ontologies. Our pro-
posal is developed in the KAON ontology editor, that allows to handle ontology concepts in an high-level
An ontology is a formal conceptualization of a partic-
ular domain of interest shared among heterogeneous
applications. It consists of entities, attributes, rela-
tionships and axioms to provide a common under-
standing of the real world (Lammari and Mtais, 2004;
Gruber, 1993; Guarino and Giaretta, 1995). With the
support of ontologies, users and systems can commu-
nicate with each other through an easier information
exchange and integration (Soo and Lin, 2001). On-
tologies help people and machines to communicate
concisely by supporting information exchange based
on semantics rather than just syntax.
There are ontological applications where informa-
tion is often vague and imprecise. For instance,
the semantic-based applications of the Semantic Web
(Berners-Lee et al., 2001), such as e-commerce,
knowledge management, web portals, etc. Indeed, the
conceptual formalism supported by a typical ontol-
ogy may not be sufficient to represent uncertain infor-
mation that is commonly found in many application
domains. For example, keywords extracted by many
queries in the same domain may not be considered
with the same relevance, as some keywords may be
more significant than others. Therefore, the need of
giving a different interpretation according to the con-
text emerges.
A possible solution to handle uncertain data and,
hence, to tackle these problems, is to incorporate
fuzzy logic into ontologies. The aim of fuzzy set
theory (Klir and Yuan, 1995) introduced by L. A.
Zadeh (Zadeh, 1965) is to describe vague concepts
through a generalized notion of set, according to
which an object may belong to a certain degree (typ-
ically a real number from the interval [0,1]) to a set.
For instance, the semantic content of a statement like
“Cabernet is a deep red acidic wine” might have de-
gree, or truth-value, of 0.6. Up to now, fuzzy sets and
ontologies are jointly used to resolve uncertain infor-
mation problems in various areas, for example, in text
retrieval (Bouquet et al., 2004; Singh et al., 2004; Ab-
ulaish and Dey, 2003) or to generate a scholarly on-
tology from a database in ESKIMO (Matheus, 2005)
and FOGA (Quan et al., 2004) frameworks. However,
in none of these examples there is a fusion of fuzzy set
theory with ontologies.
The aim of this paper is to present a proposal to di-
rectly integrate fuzzy logic in ontology in order to ob-
tain an extension of the ontology that is more suitable
for solving uncertainty reasoning problems. It is a
first step towards the realization of a theoretical model
and of a complete framework based on ontologies that
are able to consider the nuances of natural languages.
In literature, a first tentative has been made in the
context of medical document retrieval (Parry, 2004)
Calegari S. and Ciucci D. (2006).
In Proceedings of the Eighth International Conference on Enterprise Information Systems - AIDSS, pages 66-73
DOI: 10.5220/0002496100660073
by adding a degree of membership to all terms in the
ontology to overcome the overloading problem. An-
other proposal is an extension of the domain ontology
with fuzzy concept (Chang-Shing et al., 2005), how-
ever only for Chinese news summarization.
This paper shows how to insert fuzzy logic during
ontology creation with KAON (KAON, 2005). This
software consists in a number of different modules
providing a broad range of functionalities centered
around creation, storage, retrieval, maintenance and
application of ontologies. KAON allows the use of
an ontology at high-level, and the relative conceptual
models are defined in a natural and easily understand-
able way.
The rest of the paper is organized as follows: Sec-
tion 2 defines a fuzzy ontology and explains how to
define and use fuzzy values in it. Section 3 presents
the ontology editor used and it is shown how to in-
tegrate it with our framework. In Section 4, we give
an overview on related works and on the next steps of
our approach.
In this section, we present a logical framework to sup-
port and to reason with uncertainty. This is a focus
aspect for all ontology-based applications where the
user is interested in information that often contains
imprecise and vague description of concepts. For ex-
ample, one may be interested in finding “a very strong
flavored red wine” or in reasoning with concepts such
as “a cold place”, “an expensive item”, “a fast motor-
cycle”, etc.
In order to face these problems the proposed ap-
proach is based on fuzzy sets theory. It has not been
chosen a particular ontology domain to explain our
theory because our goal is to fulfil all nuances of nat-
ural languages and to take into account all the differ-
ent aspects that an ontology have to consider. Our
aim is to extend an ontology editor to directly handle
uncertainty during the ontology definition, so that to
enrich the knowledge domain.
At first, let us remind the definition of a fuzzy set.
Let us consider a nonempty set of objects U, called
the universe.Afuzzy set or generalized characteris-
tic functional is defined as a [0, 1]–valued function on
U, f : U → [0, 1]. Given an object x U , f (x)
represents the membership value of x to the set f .In
the following of this section we explain how to intro-
duce fuzzy values on different objects of an ontology
and how to automatically correct them. Finally, we
give some hint on the possible applications of a fuzzy
2.1 Defining a Fuzzy Value
The first problem to tackle is how to assign a fuzzy
value to an entity of the ontology. The trade off is be-
tween understandability and precision, since (Casillas
et al., 2003)
to obtain high degree of interpretability and ac-
curacy is a contradictory purpose and, in prac-
tice, one of the two properties prevails over the
other one. Depending on what requirement is
mainly pursued, the Fuzzy Modelling field may
be divided into two different areas:
1. Linguistic fuzzy modelling The main objec-
tive is to obtain fuzzy models with a good in-
2. Precise fuzzy modelling The main objective
is to obtain fuzzy models with a good accu-
Since our goal is to be as general as possible, both
the possibilities are given to the expert: define a
precise value or a linguistic one. In the former
case the expert, while creating the ontology, de-
fines a function f :(Concepts Instance) ×
P roperties → Property
Value × [0, 1] with the
meaning that f (o, p) is the value that a concept or
an instance o assumes for property p with associated
degree. For example, in an hypothetical ontology of
cats, f(Garfield,color) = (orange,0.8) means that for
the property color, the instance Garfield, has value or-
ange with degree 0.8. Or, in a wine ontology, f(wine,
taste)= (full-bodied,0.4) means that the concept wine
has a full-bodied (the value) taste (the property) with
degree 0.4.
Clearly, there may exist situations in which no
property value is necessary for a given property.
For example, “Garfield has sense of humour with
value 0.9 cannot be correctly expressed with the
just exposed formalism. In this situation, it is neces-
sary to map a pair (concept/instance, property) sim-
ply to [0, 1], i.e., f
:(Concept Instance) ×
P roperties → [0, 1] and the above example becomes
(Garfield,sense of humour) = 0.9.
In order to simplify the nota-
tion, we can define a unique function
g :(Concepts Instances) × (P roperties
val) → [0, 1]. Thus, “Garfield has color
orange with value 0.8 becomes g(Garfield,orange) =
0.8. Using these function g, the expert has the chance
to choose a membership value with infinite accuracy,
that is precision is preferred to interpretability.
On the other hand, the second possibility is to
choose as membership value, a label in a given set.
We have chosen the set L ={little, enough, moder-
ately, quite, very, totally} which is clearly not exhaus-
tive of all the possible labels, but it can intuitively be
modified as desidered.
In this case the value g(o, p) is automatically as-
signed according to Table 1.
Table 1: assignement of fuzzy value to labels.
Label Value
little 0.2
enough 0.4
moderately 0.6
quite 0.7
very 0.8
totally 1
Summing up, we give the chance to add a mem-
bership value to a pair (concept/instance, property) in
two different ways: through a precise value v [0, 1]
or choosing a label in the predefined set L. Thus,
through the function g we define a new relation in the
ontology domain.
Another possibility is to assign a fuzzy value to an
entity (concept or instance). This can be useful to
overcome the problem of overloading as outlined in
(Parry, 2004) and explained in Section 2.3. In this
case the expert can define a function h : Concepts
Instances → [0, 1].
Let us remark that the fuzzy value assigned using
one of the two functions g and h is a number in the
unit interval [0, 1], that is, the usual support of a many
valued logic. Hence, applications based on fuzzy on-
tologies can use this value taking advantage of stan-
dard and well-studied tools. For instance, in order to
put together two (or more) different fuzzy values, an
aggregation operator (Calvo et al., 2002) can be used.
Typical examples are t–norm and t–conorms (Kle-
ment et al., 2000), that is, binary mappings which give
a semantic to the “OR”, AND” operators. The most
known are G
odel norm and conorm, i.e., the min–max
operators. Considering the above example, it may be
necessary to compute the truth value of the statement
“Garfield is orange AND has sense of humour”. If it
is known that f(Garfield,orange)=0.8 and f(Garfield,
of humour) = 0.9 then [f(Garfield,orange)
AND f (Garfield, sense
of humour)] = min{0.8,0.9}
= 0.8.
Finally, we can give the definition of fuzzy ontol-
Definition 1. A fuzzy ontology is an ontology ex-
tended with fuzzy values which are assigned through
the two functions
g :(Concepts Instances) × (P roperties
val) → [0, 1] and
h : Concepts Instances → [0, 1].
2.2 Updating a Fuzzy Value
Once an expert has created a fuzzy ontology, it is not
realistic to assume that it is perfect and that any fuzzy
value is well-defined and suited to any environment.
Thus, a mechanism to change fuzzy values in order to
fit them in the best way to a specific environment or, in
general, to make them more correct is needed. Here,
we propose a method to update fuzzy values accord-
ing to results of some queries on some documents. We
do not enter into details about how syntactically spec-
ify queries, but we assume that we are able to perform
them and that their results are available to us.
Let us suppose that the current fuzzy value is f and
as a result of a query it must be updated to f
. The
simpliest possibility is to set f := f
. However,
it is reasonable to suppose that after some queries the
fuzzy property has reached a stable value, hence it is
not useful to change it with f
, losing all the his-
tory of the acquired knowledge. A solution can be to
diminish the importance of f
at any change:
f := f +
Q +1
where Q is the number of updates perfomed for that
value. Clearly, the value Q must be stored in the on-
tology for any defined fuzzy value.
Now, the issue is how to compute a new fuzzy
value f
. It is unlikely to find in a document a
precise definition of a fuzzy value, but usually a lin-
guistic qualifier can be found. For example, we do
not find “Cabernet has a dry taste with value 0.6”, but
it make sense a document such “Cabernet has a very
dry taste”. So a method to make use of this kind of
information is needed. Here we propose an approach
based on concept modifiers (Zadeh, 1972).
A concept modifier has the effect to alter the fuzzy
value of a property. Given a set of linguistic hedges
such as “very”, “more or less”, “slighty”, a concept
modifier is a chain of one or more hedges, such as
“very slightly” or “very very slightly”. To any (lin-
guistic) concept modifier it is necessary to associate a
(numerical) membership modifier.
Definition 2. A membership modifier is a value β>0
which is used as an exponent to modify the value of a
membership function f as f
According to their effect on a fuzzy value, a hedge
can be classified in two groups: concentration type
and dilation type. The effect of a concentration mod-
ifier is to reduce the grade of a membership value.
Thus, in this case, it must be β>1. For instance, to
the hedge “very”, it is usually assigned β =2. So,
if we know that g(Cabernet, dry
taste)=0.8, i.e.,
“Cabernet has a dry taste with value 0.8”, then Caber-
net has a very dry taste with value 0.8
the contrary a dilation hedge has the effect to raise a
membership value, that is β (0, 1). For instance,
if to slightly it is assigned β =0.25 and g(Cabernet,
taste)=0.8, then Cabernet has a slightly dry taste
with value 0.8
=0.95 according to the intu-
ition that if something is “dry” then it is even more
“slightly dry”. Let us remark that this approach is dif-
ferent from the original Zadeh’s one (Zadeh, 1972),
where “slightly”, as well as other modifiers, is han-
dled in a more complicated manner. This method has
the advantage to give a uniform and simply way to
manage concept modifiers, even if, a deeper study
about the semantic of this way of handling chain of
modifiers is needed.
So, a concept modifier is used in literature to de-
fine a new fuzzy membership given an already exist-
ing one. For example, if we know the fuzzy value of
property red we can infer the fuzzy membership of
property very red simply by raising to the power 2 the
value of red (see the above examples). However, here
we are in the opposite situation. As an example, let us
suppose to know, from an ontology, the red property
and also, as a result of a query, that a certain object
is “very red”. Hence, from very red we need to in-
fer a new red property (before “red” was fixed, here
it changes) for that object and clearly if an object is
very red it is even more red. So, if in the ontology
g(o, red)=0.7, we must increase this value, for ex-
ample g(o, red)=0.7
. In conclusion, the effect of
very is to raise the value of the property it is referred
to and not to reduce its magnitude. In a schematic
way, it is possible to say that in the usual case it is
performed the deduction
red very red
whereas in this situation:
red and very red red
This argument also applies to all the other concept
modifiers. Thus, in our case what is usually consid-
ered as a concentration modifier becomes a dilation
one and vice versa.
Two issues need now to be faced: decide which
modifiers we consider (and which are their values)
and define a method to compute β values for chains
of concept modifiers.
About the former problem, the chosen set of hedges
is H ={very, much more, more, more or less, moder-
ate, slightly}. This is only one of the possible choices.
The set H can be changed according to one
s needs, on
condition that it satisfies the following two properties.
The set H is totally ordered, i.e., very < ... <
slightly and only the β value for the smaller and
greater elements are fixed, respectively as 0.5 and
The two subsets of contraction hedges {more or
less, moderate, slightly} and dilation hedges {very,
much more, more} have the same cardinality.
These two conditions are due to the fact that we pro-
pose to adopt the algorithm presented in (Khang et al.,
2002) in order to compute the membership modifier
of a sequence of hedges. The only difference is the
order inversion of the hedges, this is due to the use we
are doing of concept modifiers which is, as explained
above, opposite to the original approach.
Moreover, we consider also the further modifier
not which behaves as the standard involutive nega-
tion on fuzzy sets: not(x):=1 x.Asanex-
ample let us suppose that g(Cabernet,dry
then if in a document it is found that “Cabernet has
not a dry taste” the new value is g
taste) =1 0.8=0.2. This way of han-
dling the not connective cannot be easily applied to
chains of hedges. Using the same example, if we
find that “Cabernet has not a very dry taste”, the new
value is g
(Cabernet, dry taste)=1
0.11. However, “not very dry induces to think to
something which is dry but not at an high degree
and this is not correctly mirrored by g
taste)=0.11. In (Singh et al., 2004) a solution to
integrate not in the set H of all concept modifiers is
presented. This solution does not seem to us a good
one, since it cannot be applied directly to a property,
but only to another concept modifier and also in this
case it can generate a negative β if the original algo-
rithm of (Khang et al., 2002) is not modified. Thus,
handling chains of modifiers which include not is left
as an open problem. Pacholczyk et al. dedicated sev-
eral works to the problem of linguistic negation (see
for instance (Pacholczyk, 1998; Pacholczyk et al.,
2002)). So an interesting future work would be the
integration of those studies in our approach.
Another open problem is that the set H of concept
modifiers is certainly not exhaustive of all the nuances
of natural language. Lots of elements could be added
to H and this will require new algorithms to handle it,
since not all existing concept modifiers can be totally
ordered or exactly split into two subgroups of same
2.3 Examples of Application
In this section we give two examples of a possible use
of fuzzy ontologies. The first one is based on fuzzy
values associated to (instance, properties) pairs and
the second one is a way to use concepts with fuzzy
values to remedy the overloading problem.
Extending queries When performing a query on a
document, it is a usual practice to extend the set of
concepts already present in the query with other ones
which can be derived from an ontology. Tipically,
given a concept, also its parents and children can be
added to the query and then searched in the document.
A possible use of fuzzy ontology is to extend
queries with, besides children and parents, instances
of concepts which satisfies to a certain degree the
query. Let us explain it with an example. We are given
a clothes ontology and a query looking for “a very
long and black coat”. In the ontology there are two
instances of coat: X which has property “long” with
value 0.7 and Y which has property “long” with value
0.3. Thus, it is natural to extend the original query
adding, not only parents and children of the concept
“coat”, but also the instance X, because long =0.7
can be interpreted as “very long”. On the other hand,
the instance Y is not added to the extended query
since long =0.3” does not mean “very long”.
To make a choice on which instances have to be
added to the extended query, we have to decide how
linguistic labels are mapped to numerical values. The
solution is again as in Section 2.1, that is only label
belonging to set L are admitted in queries and they
are mapped to numerical values according to Table 1.
If c is a concept, p is a property and l a label then
µ(c, p, l) is the value given to the label l for property
p and concept c. For instance in the above example,
the property “a very long coat” is translated to µ(coat,
long, very) =0.8. Now, we consider all the instances
i of the concept c and they are included in the ex-
tended query if and only if :
|µ(c, p, l) g(i, p)|≤ (2)
where [0, 1] is a level of tolerance. Obviously,
the number of instances to be added to the extended
query depends on the value of , the greater is
most are the instances. The boundary cases are =0,
only the instances that exactly match the query are
included, and =1, all the instances are included.
Coming back to the example, if we fix =0.2, then,
|µ(coat, long, very) g(X, long)| =0.8 0.7=
0.1 0.2=, whereas |µ(coat, long, very)
g(Y, long)| =0.8 0.3=0.5 0.2=. Hence, X
is included in the extended query and Y is not.
Clearly, this is the simplest case where only one
property is present in the query. If two or more request
must be satisfied, a generalization of equation (2) is
needed. Let us suppose that in the query there are
n properties referred to the same concept c, then in-
stance i is considered iff
|µ(c, p
) g(i, p
That is we require that the mean value of the distances
between the values of the properties in the query and
the values of the properties in the instance is less than
the tolerance .
Overloading of concepts As anticipated in Sec-
tion 2.1 a possible use of the fuzzy value associated to
concepts is to limit the problems due to overloading
of a concept in an ontology. The solution we are go-
ing to expose has been proposed in (Parry, 2004). In
our opinion this approach is more related to statistics
than to fuzzy logic, nevertheless it can be managed by
our fuzzy ontology.
Let us suppose that a concept c is present in dif-
ferent parts of the ontology, the aim is to give an in-
dication about which place is more significant with
respect to a certain domain. At a first stage, to any
concept which is present in multiple locations is given
an equal fuzzy value such that they sum up to 1. For
instance, if c is present in 4 places, respectively de-
noted as c
then we have h(c
)=0.25. For any c
the set of its local terms L
, i.e., parents and children
in the ontology, is computed. Then, all the elements
l L
are searched in the documents under analysis
and a weight w
is assigned to them according to the
relevance they have in the document. Let us suppose
that in the document under investigation, there are l
occurencies for the element l. Then, for any concept
and for any document d the following function is
The sum over all n documents of µ
is denoted as µ:
. Then, the new membership value
for concept c
and document d is:
These values are then used to update h(c
) according
to Equation 1 and they are applied in order of rele-
vance, so that a value due to a more relevant docu-
ment is applied first and it has a greater influence than
the following ones.
The KAON project is a meta-project carried out at the
Institute AIFB, University of Karlsruhe and at the Re-
search Center for Information Technologies (FZI).
KAON includes a comprehensive tool suite allow-
ing easy creation, maintenance and management of
ontologies. Furthermore, it provides a framework for
building ontology-based applications. An important
user-level application supplied by KAON is an on-
tology editor called OI-modeler. It allows to handle
entities of an ontology in a natural way. The most im-
portant features of the OI-modeler are its support for
manipulation of large ontologies and the support for
user-directed evolution of ontologies. Ontologies can
be simultaneously edited by multiple users (AA.VV.,
2004). The ontology navigation is more easy through
graph-based and tree-based metaphors.
In the last years, KAON has been used in many
areas like e-commerce and b2b applications (Motik
et al., 2002), autonomic and self-healing, self-
configuring computational system (Stojanovic et al.,
2004) and more recently, it has been applied to the Se-
mantic Web (Bozsak et al., 2002; Oberle et al., 2005).
Meal Course
Wine Grape
Wine Region
Consumable Thing
full, medium, light
red, rosate, white
delicate, moderate, strong
dry, sweet, offdry
property value
Figure 1: Wine ontology.
3.1 Ontologies in KAON
An ontology in KAON consists of concepts (sets of
elements), properties (specifications of how objects
may be connected) and instances grouped in reusable
units called OI-models (ontology-instance models)
(AA.VV., 2004). The conceptual model proposed al-
lows to define an entity in different ways, depend-
ing on the point of view of the observer. That is,
an entity can be interpreted as a concept, as well as
an instance. Moreover, property instantiation must be
in accordance with the domain and range constraints
(i.e. axioms, general rules, value-allowed) and must
obey the cardinality constraints, as specified by the
property specifications. An OI-model may include
other OI-models, and have immediate access to all de-
finitions from the included model.
Figure 1 is an example of an ontology in KAON:
it represents only a partial ontology definition about
wine. We have chosen such ontology because it is
largely widespread and known, and so it is more
simply to understand the reasoning approach used in
In KAON language, it is possible to define well-
known symmetric, transitive and inverse proper-
ties, with the addition of modularization and meta-
modeling (AA.VV., 2004). Obviously, each of these
features allow to manage two types of implicit knowl-
edge: axioms and general rules. The formers are a
standard set of rules, such as the transitive properties,
the latters are general rules to combine and to adapt
information defined in an ontology domain.
Moreover, KAON language allows to specify so-
called lexical entries (i.e. labels, synonyms, stems, or
textual documentation) which reflect various nuances
of natural languages. For example, the same lexical
entry may be associated with several elements: the
label BEAR may be associated with an instance rep-
resenting a bear as an animal or as a puppet. Further-
more, the instances can be defined in different lan-
guages, namely English, German, French, Spanish,
Portuguese, Arabic and Chinese.
3.2 Fuzzy Ontologies in KAON
Our aim is to enrich KAON language adding the pro-
posed fuzzy-sets approach. In the following, it is
showed how we have integrated our framework in the
KAON project.
Figure 2: New KAON ontology overview.
Figure 2 represents a “Fuzzy Inspector” developed
to create in KAON the fuzzy ontology. The new panel
has been called “Fuzzy Logic” (see right lower corner
in Figure 2) and it allows the expert an easy fuzzy
logic integration. The Fuzzy Inspector is composed
by a table representing fuzzy entity, membership de-
gree and number of updates Q.
The domain expert can choose his fuzzy entity
(concept or instance) simply clicking up through two
types of interface proposed by KAON, namely graph-
based and tree-based metaphors, partially showed in
the screenshot. Moreover, the expert can select the
link between an instance and a property adding its
fuzzy value.
Thus, the expert can create real fuzzy ontology do-
main selecting the entity and directly inserting fuzzy
logic through the Fuzzy Inspector Panel purposely de-
veloped. In Figure 2, we propose two ways to use the
Fuzzy Logic Panel. In the first row the expert types
the membership degree according to his point of view.
In the second row he can choose the apposite value by
a list. The selected element in the list will be referred
to an a-priori defined numerical value as explained in
Section 2.1. In the definition phase of the ontology
the number of the updates is zero. This value will
be changed during the queries in accordance with the
functions defined in previous sections.
KAON’s ontology language is based on RDFS
(RDFS, 2004) with proprietary extensions for al-
gebraic property characteristics (symmetric, transi-
tive and inverse), cardinality, modularization, meta-
modelling and explicit representation of lexical infor-
In literature, all the limits about the RDFS are
well-known. Thus, it has been developed KAON2
(KAON2, 2005) that is a successor of the KAON
project. The main difference as to previous KAON
version is the supported ontology language, namely
KAON used a proprietary extension of RDFS,
whereas KAON2 is based on OWL DL (OWL, 2005).
OWL DL is a sublanguage of OWL (OWL, 2005)
and it supports those users who want the maximum
expressiveness without losing computational com-
pleteness (all conclusions are guaranteed to be com-
puted) and decidability of reasoning systems (all com-
putations will finish in finite time).
In more details, KAON2’s language is based on a
combination of the OWL DL and OWL Lite sublan-
guages (KAON2, 2005) of the OWL Web Ontology
Language (OWL, 2005).
Recently, some proposals to integrate fuzzy logic
in OWL have been presented (Straccia, 2005; Stoilos
et al., 2005; Pan et al., 2005).
The more complete and suitable to our study
seems to be the extension of SHOIN (D) presented
in (Straccia, 2005).
Thus, the next and last step to the integration of
fuzzy ontology in KAON2 is a deeper analysis of all
these approaches and the adaptation of one of them to
our situation. This is out of the scope of the present
paper and will be proposed in a forthcoming work.
In this paper, we have introduced fuzzy logic directly
in the ontology during the domain definition, enrich-
ing the actual features proposed by other ontology ed-
itors. The proposed solution allows to represent and
to reason with uncertain information. This is a deli-
cate problem for all those areas where the applications
are based on ontology.
The domain expert has two possibilities to add a
membership value in an ontology domain: through a
pair ({concept,instance},property) or through an en-
tity {concept, instance}. In both solutions, he/she can
assign this degree through a precise value v [0, 1]
or choosing a label in the predefined set L.
We have also proposed a method, based on con-
cept modifiers, to automatically update the member-
ship degree during queries, useful, as example, for the
extraction of more relevant documents.
Furthermore, we have presented two possible ex-
amples of application: to extend a query and to over-
come the problem of overloading.
KAON has been the ontology editor chosen to in-
troduce fuzzy logic during the ontology definition.
We have integrated fuzzy logic in KAON, developing
a suitable Fuzzy Inspector Panel.
In the future, it is necessary to develop fuzzy-OWL
in KAON2 and to test all the proposed framework.
Furthermore, we plan to enrich our theory considering
linguistic negation. This is another crucial topic in
order to handle all the uncertainty situations proposed
by natural languages within the ontological domain.
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