Ontology of Imprecision and Fuzzy Ontology Applications

Robin Wikström

IAMSR, Åbo Akademi University, Joukahaisenkatu 3-5 A, FIN-20520 Turku, Finland

Keywords:

Web Application, Fuzzy Ontology, OWA Operators, f uzzyDL, Java.

Abstract:

Dealing with uncertainty and vagueness is an important challenge for the Semantic Web. Ontologies are

regularly used for structuring knowledge for the Semantic Web, however, the traditionally used ontologies

are not suitable for all contexts. Introducing fuzzy logic offers new possibilities. In this paper an overview

regarding ontology of imprecision is presented and a web application, based on the Fuzzy Wine Ontology is

constructed. The paper provides some indications on how fuzzy ontologies can offer better and more reliable

solutions. The web application opens the door for future developments in the knowledge mobilization ﬁeld.

1 INTRODUCTION

Recently, the development of the Semantic Web has

revealed that there is a demand for new methods. This

observation becomes crucial especially regarding on-

tologies, as the current ontologies have limitations

when dealing with uncertain and vague knowledge,

which is present in most practical applications; but

there is a tendency to forget about this resource. Tacit

knowledge can exist in the form of linguistic informa-

tion or historical data. In organizations, tacit knowl-

edge disappears, for instance, when expert employees

retire. Storing and thereby enabling for continuous

use of this knowledge is therefore a key issue in or-

ganizations. There is also a challenge regarding the

practicality of ontologies, as they might become dif-

ﬁcult to maintain over time. Traditional methods are

difﬁcult to update and maintain in the long run, as

they consist of a network of nodes (creating the on-

tology), which implies that even a small change on a

low level results in numerous changes throughout the

ontology.

The Semantic Web has traditionally been based on

different types of crisp description logics (DL), which

are not suitable for dealing with uncertainties. Fuzzy

logic and fuzzy ontologies provide a solution to this

issue. Machacha and Bhattacharya (2000) observe

that fuzzy logic enables computers to imitate the hu-

man reasoning process, utilizing imprecise informa-

tion but still making precise decisions.

In this paper, we provide an overview of ontolo-

gies of imprecision (also known as fuzzy ontologies)

by shortly presenting the latest research in the ﬁeld as

well as some software and applications that have re-

cently been developed.

A web application, combining the Fuzzy Wine

Ontology (Carlsson et al., 2012b,a) with the fuzzyDL

reasoner (Bobillo and Straccia, 2011) and web tech-

niques is presented. The application shows that fuzzy

ontology can be used for real-life problems, in the

presence of tacit and vague knowledge / data. The

Fuzzy Wine Ontology provides an appropriate tool

to handle vagueness inherent in this context, as the

description of wines naturally consists of a number

of imprecise attributes, expert-based knowledge, the

produced results are, however, precise.

This paper is structured as follows. Section 2

presents a short literature review regarding ontologies

of imprecision. Section 3 presents the web applica-

tion and, ﬁnally, Section 4 includes a conclusion and

some discussion about future research.

2 LITERATURE REVIEW

This section presents a literature review regarding the

main components of the proposed model.

2.1 Ontology

Ontologies have different roles depending on the con-

text they function in for the Semantic Web; they rep-

resent the main technology for creating interoperabil-

ity on the semantic level. This is achieved by creating

a formal illustration of the data, which thanks to its

284

Wikström R..

Ontology of Imprecision and Fuzzy Ontology Applications.

DOI: 10.5220/0004361002840287

In Proceedings of the 9th International Conference on Web Information Systems and Technologies (WEBIST-2013), pages 284-287

ISBN: 978-989-8565-54-9

 2013 SCITEPRESS (Science and Technology Publications, Lda.)

formality can be shared and reused all over the Web.

An ontology formulates and models the relationship

between the concepts in a given domain (d‘Aquin and

Noy, 2012). An ontology could also be seen as a com-

plex, domain speciﬁc vocabulary, that organizes and

integrates data. In this way, it becomes possible to

link together all the information available on the Web,

as well as to include sources such as public libraries

(Hebeler et al., 2011).

2.2 Fuzzy Logic

Fuzzy sets theory and fuzzy logic were originally pro-

posed by Zadeh (1965), who points out that objects

in the real world seldom have clearly-deﬁned mem-

berships to groups. In classical set theory, elements

can exclusively belong to a set, or not, but with fuzzy

set theory it becomes possible for elements to belong

to different sets to some degree. This does not mean

that the answers automatically are vague or imprecise.

Fuzzy logic makes it possible to reason also in the

grey areas, with the use of a simple numerical idea,

dealing with ambiguity and still producing precise an-

swers (Kordon, 2009).

Deﬁnition 1. Let X be a nonempty set. A fuzzy subset

A of X is characterized by its membership function

: X → [0, 1]

where µ

(x) is interpreted as the degree of member-

ship of element x in fuzzy set A for each x ∈ X.

2.3 Fuzzy Ontologies

In recent years, fuzzy ontologies have started to at-

tract an increased interest from the academic world,

although fuzzy logic was introduced already in the

1960‘s (Zadeh, 1965). However, research about fuzzy

ontologies did barely exist before the start of this cen-

tury, even though Peña (1984) already in the 1980‘s

stated that using fuzzy logic in ontologies would be

more suitable in certain cases, compared to classical

logic. Lately, this statement has been supported sev-

eral times; Sanchez (2006) argues that classical on-

tologies are not appropriate for dealing with imprecise

and vague knowledge, which is a crucial problem for

several real world domains.

Even though current knowledge representation

formalisms for the Semantic Web rely on crisp logic,

it does not mean that all knowledge is crisp. It has be-

come evident that fuzzy ontologies could provide op-

portunities for new applications aimed for the Seman-

tic Web, especially in ﬁelds where vague knowledge

is imminent. It is clear that there is a lot of unexplored

potential in this research ﬁeld.

Recently, there has been some development re-

garding software and reasoners aimed at fuzzy ontol-

ogy creation. The f uzzyDL reasoner by Bobillo and

Straccia (2008) is a description logic reasoner, includ-

ing support for fuzzy logic. FuzzyDL extends the DL

SHIF with fuzzy concepts. For instance, it allows

the user to deﬁne fuzzy concepts with left-shoulder,

right-shoulder, triangular and trapezoidal member-

ship functions. It also supports both Lukasiewicz

logic and "Zadeh semantics" (Bobillo and Straccia,

2011).

Bobillo et al. (2012) have created a different rea-

soner with support for fuzzy logic, similar to the

f uzzyDL reasoner. DeLorean (DEscription LOgic

REasoner with vAgueNess) is a Description Logic

reasoner which also supports fuzzy rough sets (fuzzy

rough extensions of the fuzzy DLs SROIQ(D) and

SHOIN(D), which are equivalent to OWL and OWL

2).

Stoilos et al. (2005) developed a fuzzy reasoning

engine, FiRE, based on the fuzzy description logic f-

SHIN. The engine has been used for several Semantic

Web applications and there are plans to develop FiRE

towards supporting also fuzzy OWL-DL.

Another relevant software is SoftFacts by Straccia

(2010), an ontology mediated database system. Pro-

viding the possibility to include ontology layers in

databases, SoftFacts supports MySQL, Postgres and

RankSQL as well as several sets of OWL QL proﬁle

language expressions.

Calegari and Ciucci (2007) managed to enrich the

KAON language, making it possible to express fuzzy

ontologies with KAON. However, KAON ontologies

are based on RDFS which have limitations in compar-

ison with OWL. A solution presented for this problem

is to convert the KAON ﬁle to an OWL ﬁle.

3 THE WEB APPLICATION

A web application has been developed based on the

Fuzzy Wine Ontology. The goal of the web appli-

cation is to show that it is possible to make use of

tacit knowledge (available internally in organizations)

and create usable applications for industrial purposes.

This Section is a short presentation on how the appli-

cation was structured and what results it produces.

Initially deﬁned by Carlsson et al. (2012b,a), the

Fuzzy Wine Ontology has now been applied to OWL

by using Protégé. The data stored in the ontology

is based on expert knowledge, retrieved from litera-

ture and forums written by wine connoisseurs. The

structure of the fuzzy wine ontology makes it possi-

ble to combine both crisp values and fuzzy values;

OntologyofImprecisionandFuzzyOntologyApplications

285

Figure 1: Screen shot from the Web Application Front Page.

for instance, the crisp value “wine color”and the lin-

guistics expressed “sweet”describing the wines taste.

The wine characteristics are combined through aggre-

gation, using the ordered weighted averaging opera-

tor. The wine combinations are used for selecting the

best wine for speciﬁc scenarios. According the wine

connoisseurs, different contexts, for instance, eating

game together with your family, require a different

kind of wine, compared to eating ﬁsh at a business

dinner.

Deﬁnition 2 ((Yager, 1988)). An OWA function is a

mapping OWA

: [0, 1]

→ [0, 1] with an associated

vector w = (w

, . . . , w

) such that

∑

i=1

= 1 and

∈ [0, 1] ∀i.

Furthermore,

OWA

, . . . , a

) =

∑

i=1

(i)

where a

( j)

is the j-th largest element of the multiset

A =

, . . . , a

3.1 Technology Framework

The technological framework for the web application

consists of the fuzzyDL reasoner developed by Bo-

billo and Straccia (2011). The fuzzyDL reasoner uses

the Gurobi optimizer for calculation purposes and the

Java programming language for connecting the rea-

soner with the server. The server uses HTML and

Glassﬁsh for processing the users‘ requests.

3.2 The Fuzzy Wine Ontology

Figure 1 shows a screenshot from front-page with the

different alternatives available. The user chooses the

context and the speciﬁc food. In this example, the

user prefers a wine that suites a candle dinner where

the user plans to serve game. The query is then sub-

mitted to the server, where it is processed by fuzzyDL.

The result is then displayed as an HTML page.

The OWA operators for this example are deﬁned

in the following way:

Candle: 0.4 MediumPrice, 0.3 LowAcidity,

0.3 HighAlcohol

Game: 0.25 HighAlcohol, 0.25 HighAcidity,

0.25 Red (color), 0.25 Full (body)

OWA combining Candle and Game:

0.5 Candle 0.5 Game

The following example presents how one mem-

bership value is calculated for one wine. First, all the

membership values for different concepts are calcu-

lated, this example shows Fenocchio Barolo member-

ship value for HighAlcohol:

Wine: Fenocchio Barolo. Full bodied red wine. Alcohol

level: 14 Acidity level: 5.4 Price: 26,5 C Concept: High-

Alcohol, Rightshoulder function

Figure 2: Deﬁning the membership value of Fenocchio

Barolo.

Fenocchio Barolo‘s membership value

to HighAlcohol = 0.75

Then, all the different membership values are com-

bined:

(0.4 * 0.0) + (0.3 * 0.09) + (0.3 * 0.75) = 0.252

(0.25 * 0.75) + (0.25 * 0.14) +

(0.25 * 1.0) + (0.25 * 1.0) = 0.7225

(0.5 * 0.252) + (0.5 * 0.7225) = 0.48725

Fenocchio Barolo membership value for the

candle/game context is: 0.48725

In this case, the top 5 most suitable wines

turned out to be: Villages Cuvee 3 Fleurs (mem-

bership value of 0.883), Abadal Cabernet Sauvi-

gnon Reserva (0.881), Domaine Depeyre (0.823),

Belleruche (0.717), Baron de Ley Reserva (0.713).

With this approach, also a wine that is far from

suitable, regarding a speciﬁc property, can be situated

in a top spot. If one would use an approach based

on crisp logic only, it would ﬁlter out wines that are

almost perfect, but do not fulﬁl a certain property. For

instance, if one requires that the wine should be from

year 2009, among other properties, it automatically

would ﬁlter out wines from 2008 and 2010, even if

they would full-ﬁll all the other demands. By using

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fuzzy logic, a wine produced in year 2008 or 2010

would still be considered and not be eliminated from

the search already in an early stage.

4 CONCLUSIONS

In this article, we present a short literature review

about fuzzy ontologies. In recent years, there have

been several successful applications of fuzzy logic

and ontologies. The fact that fuzzy logic can deal

with uncertain and imprecise knowledge in a more ef-

ﬁcient way, compared to traditional methods, is a key

factor for encouraging future development. Research

results prove that applications and systems based on

fuzzy logic and ontologies have the possibility to cap-

ture and model tacit knowledge. This could limit the

loss of expert knowledge, for instance, as employees

disappear from organizations.

A web application, based on the techniques and

methods developed by Bobillo and Straccia (2011)

and Bobillo and Straccia (2008) in combination with

Java, Gurobi, HTML and Protégé, is also presented.

The application can be accessed and used through a

web browser. As the need for accessing relevant in-

formation wherever and whenever one needs it is in-

creasing, the mobility issues will certainly be impor-

tant factors for future applications. This web applica-

tion shows that fuzzy ontologies and fuzzy reasoners

can be accessed and used through web browser; in

other words, the application is made platform inde-

pendent.

Future directions for the fuzzy ontology ﬁelds

seem to be centred around the combination between

fuzzy logic and the Web Ontology Language (OWL).

The latest research and ﬁndings on type-2 fuzzy logic

together with ontologies should spark future research

about type-2 fuzzy logic based ontologies, as this

combination improves the possibilities to model un-

certainty (Lee et al., 2010). Exploring how this recent

development could facilitate future knowledge mobi-

lization applications and systems is therefore the cen-

tral theme for future research.

ACKNOWLEDGEMENTS

A special thanks to Prof. Christer Carlsson (IAMSR)

and Dr. József Mezei (IAMSR) for valuable advices

regarding the article.

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