Expert Systems with Applications 37 (2010) 6052–6060

Contents lists available at ScienceDirect

Expert Systems with Applications

journal homepage: www.elsevier .com/locate /eswa

Representation and reasoning of context-dependant knowledge in distributedfuzzy ontologies

Yuncheng Jiang a,b,*, Yong Tang a, Ju Wang c, Suqin Tang c

a School of Computer Science, South China Normal University, Guangzhou 510631, PR Chinab State Key Laboratory of Computer Science, Institute of Software, Chinese Academy of Sciences, Beijing 100190, PR Chinac School of Computer Science and Information Technology, Guangxi Normal University, Guilin 541004, PR China

a r t i c l e i n f o a b s t r a c t

Keywords:Knowledge representation and reasoningContext-aware systemsFuzzy ontologiesDistributed ontologiesDescription logics

0957-4174/$ - see front matter � 2010 Elsevier Ltd. Adoi:10.1016/j.eswa.2010.02.122

* Corresponding author. Tel.: +86 2085211352 306E-mail addresses: ycjiang@scnu.edu.cn, jiangyc@ic

Most of current knowledge based systems manage impressive amounts of information (especially distrib-uted fuzzy information). In addition to widely pointed-out integration and maintenance difficulties, othercommon problem is overwhelming of users with much more information than the strictly necessary forfulfilling a task. This issue has been pointed out with the name of ‘‘information overload”. Use of contextknowledge has been envisioned as an appropriate solution to deal with this information overload matter.In this paper, we present a distributed fuzzy context-domain relevance (DFCDR) model for representationin fuzzy ontologies relevance relations between fuzzy context ontology and distributed fuzzy domainontologies. In fact, the DFCDR model is a distributed fuzzy extension of the context-domain relevance(CDR) model.

� 2010 Elsevier Ltd. All rights reserved.

1. Introduction

Emerging ubiquitous or pervasive computing technologies offer‘‘anytime, anywhere, anyone” computing by decoupling users fromdevices (Bobillo, Delgado, & Gomez-Romero, 2008; Hong, Suh, &Kim, 2009; Hong, Suh, Kim, & Kim, 2009; Kwon, 2009). To provideadequate services for the users, applications and services should beaware of their contexts and automatically adapt to their changingcontexts – known as context-awareness (Bolchini, Schreiber, &Tanca, 2007; Feng, Teng, & Tan, 2009; Hong et al., 2009; Kang,Suh, & Yoo, 2008; Kim, Lee, Oh, & Choi, 2009). Context is any infor-mation that can be used to characterize the situation of an entity.An entity is a person, place, or object that is considered relevant tothe interaction between a user and an application, including loca-tion, time, activities, and the preferences of each entity (Dey, 2001;Hong et al., 2009). Context-awareness means that one is able to usecontext information. A system is context-aware if it can extract,interpret, and use context information and adapt its functionalityto the current context of use (Byun & Cheverst, 2004). The termcontext-aware computing is commonly understood by those work-ing in context-aware, where it is felt that context is a key in theirefforts to disperse and transparently weave computer technologyinto our lives. One goal of context-aware systems is to acquireand utilize information on the context of a device in order to pro-vide services that are appropriate to the particular people, place,

ll rights reserved.

.s.ict.ac.cn (Y. Jiang).

time, event, etc. These systems aim to provide context-aware ac-cess to information, communication, and computation (Honget al., 2009).

On the other hand, most of current knowledge based systems(KBSs) manage impressive amounts of information (or resources),ranging from local databases to resources imported form theWeb. In addition to widely pointed-out integration and mainte-nance difficulties, other common problem is overwhelming ofusers with much more information than the strictly necessary forfulfilling a task, forcing them to dig in a list of results to find valu-able answers. This issue has been pointed out in the literature withthe name of ‘‘information overload” (Eppler & Mengis, 2004). Thus,the challenge for KBS technologies is to support tailoring and sum-marizing of information collected from massive, heterogeneousand distributed sources depending on user needs (Farhoomand &Drury, 2002). Though it has not been so widely studied, informa-tion overload is especially critical in mobile decision support sys-tems (DSSs), since neither the capabilities of the handhelddevices nor the users’ situation are likely to ease or even permitcarrying out this manual post-processing. Hence, it is widely ac-cepted that the silver bullet for mobile knowledge delivery is smartresult filtering: to summarize available data to provide nomadicusers with the smallest amount of information that is significantfor the decision process (Bobillo et al., 2008). Recently, Bobilloet al. (2008) presented a proposal to tackle the problem of informa-tion overload, paying special attention to mobile KBSs, by usingcontext knowledge. The core of the approach is the context-do-main relevance (CDR) model, a formal pattern for representing

Y. Jiang et al. / Expert Systems with Applications 37 (2010) 6052–6060 6053

relevance of information depending on use scenarios in ontologicalknowledge bases (KBs). However, as pointed out by Bobillo et al.(2008), the CDR model is crisp, and cannot deal with fuzzy oruncertain information. Consequently, fuzzy, probabilistic, or possi-bilistic extensions to the CDR model should be considered, as theywould allow to define weighted relevance relations between con-texts and domains. Furthermore, the CDR model only considerssingle KBS (or domain ontology); in other words, it does not con-sider multiple distributed KBSs (or multiple distributed domainontologies). Hence, distributed extension to the CDR model shouldalso be considered, since decentralization of the system can turnthe clients (mobile KBSs) more intelligent, that is, able to managemore knowledge.

Let us continue to consider the hospital information system(HIS) example presented by Bobillo et al. (2008). Now we also con-sider a physician in an emergency assistance unit that is caring atthe road for a patient injured in an accident. Knowing some infor-mation about the patient’s clinical history will be as well helpful inthis situation. In other words, in this situation, a brief reportincluding those pieces of the patient’s clinical information thatought to be considered would be very valuable. The clinical proce-dure that is going to be carried out would determine which infor-mation should be part of this summary. Therefore, two differentkinds of knowledge are to be managed by such mobile system:

(i) Domain knowledge about the problem that must beresolved; this is made up by the patients’ electronic healthrecords in distributed HISs of some different hospitals. Thissituation is entirely possible, since one patient may see adoctor in different hospitals at different times, thus thereexists different electronic health records in different HISsfor the same patient. Moreover, some electronic healthrecords are fuzzy. For example, Tom is a very likely heartpatient, where the information ‘‘very likely” is fuzzy.

(ii) Context knowledge about the scenarios where the domainknowledge will be used; for our physician, this would be avocabulary to briefly describe the situation of the patienthe/she is going to attend. With the same as domain knowl-edge, context knowledge may also be fuzzy.

To state which fuzzy knowledge from the distributed HISs mustbe considered in each scenario, links between context knowledgeand distributed domain knowledge can be defined. Furthermore,the links may also be fuzzy. For instance, a link asserting that‘‘information about previous anesthetic drugs reactions” may beconsidered when ‘‘the patient has a penetrating wound” shouldbe created. Here, the link ‘‘may be” is fuzzy. To cope with the situ-ation mentioned above, we have to provide a distributed fuzzyextension of the proposal presented by Bobillo et al. (2008).

In this work, we present a distributed fuzzy extension of theCDR model to cope with the vagueness and decentralization of mo-bile KBSs, by using fuzzy context knowledge (or ontology) and dis-tributed fuzzy domain knowledge (or ontologies). That is to say, weprovide a distributed fuzzy context-domain relevance (DFCDR)model, a formal pattern for representing fuzzy (or weighted) rele-vance of information depending on use scenarios in distributedfuzzy ontological knowledge. Moreover, we present the formalsemantics of the DFCDR model, an algorithm to extract context-dependant summaries by reasoning within the distributed fuzzyontologies, and an implementation approach of the algorithm byusing description logics reasoning systems.

The rest of this paper is organized as follows. In Section 2, weprovide distributed fuzzy ontologies based on distributed fuzzydescription logics. Section 3 presents the formalization of the dis-tributed fuzzy context-domain relevance (DFCDR) model and thereasoning algorithm, and an implementation approach of the rea-

soning algorithm is provided. In Section 4, we discuss some relatedworks about environment awareness in mobile and pervasive com-puting, besides some current proposals concerning reasoning withcontexts and micro-theories in ontological representations. Finally,in Section 5, we draw the conclusion and present some perspec-tives for future research.

2. Distributed fuzzy ontologies

In this section, we present the notions of distributed fuzzyontologies. In the work presented by Bobillo et al. (2008), Bobilloet al. use ontologies (Fendel, 2001; Studer, Benjamins, & Fensel,1998; Zhang, Yoshida, & Tang, 2009) to materialize the CDR modelsince ontologies have been remarked to be a suitable formalism tobuild a KBS including context knowledge. Nowadays, propertiesand semantics of ontology constructs mainly are determined bydescription logics (DLs) (Baader, Calvanese, McGuinness, Nardi, &Patel-Schneider, 2007; Horrocks, 2008), a family of logics for repre-senting structured knowledge that have proved to be very useful asontology languages.

In this work, we will use distributed fuzzy ontologies to mate-rialize the DFCDR model. Obviously, we need to generalize the clas-sical DLs into distributed fuzzy DLs (DFDLs for short) firstly, andthen we can obtain the definitions of distributed fuzzy ontologies.Hence, in the following, we will introduce a kind of new DL, i.e.,distributed fuzzy DL formally.

As the name implies, DFDLs are the distributed fuzzy extensionsof classical DLs, or the distributed extensions of fuzzy DLs (Bobillo,Delgado, Gomez-Romero, & Straccia, 2009; Lukasiewicz & Straccia,2008; Stoilos, Stamou, Pan, Tzouvaras, & Horrocks, 2007; Straccia,2006), or the integration between distributed DLs (Borgida & Sera-fini, 2003; Serafini, Borgida, & Tamilin, 2005) and fuzzy DLs.Regarding distributed fuzzy DLs or distributed fuzzy ontologies,Li, Xu, Lu, and Kang (2006), Zhou, Lu, Li, Zhang, and Kang (2008)Grau, Parsia, and Sirin (2006) have presented several distributedfuzzy DLs (or ontologies) DEFDL, DeFSHOIN, and e-connectedOWL ontologies based on e-connections (Kutz, Lutz, Wolter, &Zakharyaschev, 2004), respectively. To adapt to the requirement,in what follows we will present a kind of new distributed fuzzyDL. The reason for restricting our attention to the new distributedfuzzy DL would be made clear in Section 3.2. From now on in thispaper, whenever we mention distributed fuzzy DLs, we will implic-itly refer to the new distributed fuzzy DLs defined below. Now wegive the syntax and semantics of the DFDLs.

Syntax: Given a non-empty set IN of indexes, used to enumeratelocal fuzzy ontologies (Tho, Hui, & Fong, 2006; Tho, Hui, Fong &Cao, 2006), let fFDLigi2IN be a collection of fuzzy DLs. We assumethe reader is familiar with fuzzy DLs and related reasoning sys-tems, as described in Bobillo et al. (2009); Lukasiewicz and Straccia(2008). There is one point we have to point out here. All fuzzy DLsmust be based on a classical DL. In distributed fuzzy DLs, theunderlying classical DL can be any (decidable) DL. For example,we can reply on fuzzy DL FSROIQ(D) (Bobillo, 2008; Bobillo et al.,2009) that is a fuzzy extension of the expressive DL SROIQ(D) (Bo-billo, 2008; Horrocks, Kutz, & Sattler, 2006) behind OWL 2 (Grauet al., 2008).

For each i 2 IN, let us denote a fuzzy TBox, fuzzy ABox, and fuz-zy RBox of FDLi as FTi; FAi, and FRi, respectively. In order to distin-guish the descriptions from various FDLi, we start by labeling themwith the index i, written as i:C. However, when talking about sub-sumption within a single FDLi, we will use the more readablehi : C v D ffl ai, instead of the formally correct hi : C v i : D ffl ai.In other words, we use hi : C v D ffl ai to say that hC v D ffl ai isbeing considered in the i-th fuzzy ontology (or fuzzy DL), whereffl stands for P; >;6, and <. Similarly for role axioms.

6054 Y. Jiang et al. / Expert Systems with Applications 37 (2010) 6052–6060

Semantic mappings between different fuzzy DLs (or fuzzyontologies) are expressed via fuzzy bridge rules. A fuzzy bridge rulefrom i to j is an expression, which in this paper is restricted tobeing one of the following four forms:

hi : C!v j : D . ai, called a fuzzy positive into-bridge rule;hi : C!w j : D . ai, called a fuzzy positive onto-bridge rule;hi : C!v j : D / ai, called a fuzzy negative into-bridge rule;hi : C!w j : D / ai, called a fuzzy negative onto-bridge rule;

where C and D are concepts, . stands for P and >; / stands for 6and <, and a 2 ½0;1�.

Fuzzy bridge rules from i to j express fuzzy subsumption rela-tions between i and j viewed from the subjective point of view ofthe jth fuzzy DL (or fuzzy ontology). For instance, the fuzzy positiveinto-bridge rule hi : C!v j : D P ai intuitively says that, from the jthpoint of view, the subsumption degree between concept C in i andconcept D in j is at least a.

If a is an individual in FDLi, while b; b1; . . . are individuals ofFDLj, then an individual correspondence from i to j is an expressionof one of the following two forms:

i : a! j : b, called a (partial) individual correspondence;i : a!¼ j : fb1; b2; . . .g, called a complete individual correspondence.

A distributed fuzzy TBox DFT ¼ hfFTigi2IN ; FBi consists of a collec-tion of fuzzy DL TBoxes fFTigi2IN , and a collection FB ¼ fFBijg, whereFBij is a set of fuzzy bridge rules from i to j, for i–j 2 IN. For everyk 2 IN, all descriptions in FTk must be in the corresponding lan-guage FDLk, and for every fuzzy bridge rule hi : C!v j : D .

ai; hi : C!w j : D . ai; hi : C!v j : D / ai, or hi : C!w j : D / ai inFBij, the concepts C and D must be in the language FDLi and FDLj,respectively.

A distributed fuzzy ABox DFA ¼ hfFAigi2IN; ICi consists of a set offuzzy DL ABoxes fFAigi2IN , and a set IC ¼ fICijgi–j2IN of partial andcomplete individual correspondences from i to j. For every k 2 IN,all descriptions in FAk must be in the corresponding languageFDLk, and for every correspondence rule i : a! j : b ori : a!¼ j : fb1; b2; . . .g in ICij, the individual name a must be in FDLi,and b1; b2; . . . in FDLj.

A distributed fuzzy RBox DFR ¼ fFRigi2IN , i.e., DFR is a collection offuzzy DL RBoxes. For every k 2 IN, all descriptions in FRk must be inthe corresponding language FDLk.

A distributed fuzzy knowledge base DFKB ¼ hDFR;DFT;DFAi con-sists of a distributed fuzzy RBox DFR, a distributed fuzzy TBoxDFT, and a distributed fuzzy ABox DFA.

Semantics: DFDL semantics is a fuzzy customization of the localmodels semantics for multi context systems (Ghidini & Giunchi-glia, 2001). Each fuzzy knowledge base FKBi ¼ hFRi; FTi; FAii is lo-cally interpreted by a fuzzy DL interpretation Ii ¼ ðDIi; �IiÞ. Ofcourse, if FKBi allows to reason with fuzzy datatype, the fuzzyknowledge base FKBi ¼ hFRi; FTi; FAii is locally interpreted by a fuz-zy DL interpretation Ii ¼ ðDIi; �IiÞ relative to a fuzzy datatype the-ory D ¼ ðDD; �DÞ. Regarding the definition of fuzzy datatypetheory, see especially (Lukasiewicz & Straccia, 2008; Straccia,2006) for further details. Since local domains may be heteroge-neous (e.g., time may be represented by Rationals and Integers intwo fuzzy ontologies), we need relations that model semantics cor-respondences between heterogeneous domains. A domain relationrij from DIi to DIj is a subset DIi � DIj. We use rijðdÞ to denotefd0 2 DIjjhd; d0i 2 rijg; for E # DIi, we use rijðEÞ for [d2ErijðdÞ.

In the rest of the paper, we will let �; �; ), and H be an arbi-trary but fixed t-norm, s-norm, implication function, and negationfunction, respectively, (see (Bobillo et al., 2009; Hajek, 1998; Luka-siewicz & Straccia, 2008) for some specific choices).

A distributed fuzzy interpretation DI ¼ hfIigi2IN ; frijgi–j2INi of DFKBconsists of fuzzy interpretations Ii for FDLi, and a set of domainrelations rij.

A distributed fuzzy interpretation DI d-satisfies (written asDI�d) the elements of a distributed fuzzy TBox DFT ¼ hfFTigi2IN;

FBi according to the following clauses: for every i; j 2 IN,

� DI�dhi : C!v j : D . ai, if infa2DIj ððrijðC0ÞÞIjðaÞ ) DIjðaÞÞ . a;

� DI�dhi : C!w j : D . ai, if infa2DIj ðDIjðaÞ ) ðrijðC0ÞÞIjðaÞÞ . a;

� DI�dhi : C!v j : D / ai, if infa2DIj ððrijðC0ÞÞIjðaÞ ) DIjðaÞÞ / a;

� DI�dhi : C!w j : D / ai, if infa2DIj ðDIjðaÞ ) ðrijðC0ÞÞIjðaÞÞ / a;

� DI�dhi : C v D ffl ai, if Ii � hC v D ffl ai, i.e., infa2DIi ðCIiðaÞ )

DIiðaÞÞ ffl a;� DI�dFTi, if Ii � FTi, i.e., for every element x 2 FTi; Ii � x;� DI�dDFT , if for every i 2 IN; DI�dFTi, and DI d-satisfies every

fuzzy bridge rule in FB;

where C0 ¼ fx 2 DIijCIiðxÞ > 0g.Finally, DFT�dhi : C v D ffl ai (read as ‘‘DFT d-entails hi : C v

D ffl ai”) if, for every distributed fuzzy interpretation DI;DI�dDFTimplies DI�dhi : C v D ffl ai. We say DFT is satisfiable if there existsa DI such that DI�dDFT . Concept i:C is satisfiable w.r.t. DFT if there isa DI such that DI�dDFT, and there is some a 2 DIi such thatCIiðaÞ ¼ a, and a 2 (0,1].

Concerning individuals, we have the following:A distributed fuzzy interpretation DI d-satisfies the elements of

a distributed fuzzy ABox DFA ¼ hfFAigi2IN; ICi according to the fol-lowing clauses: for every i; j 2 IN,

� DI�di : a! j : b, if bIj 2 rijðaIiÞ;� DI�di : a!¼ j : fb1; b2; . . .g, if rijðaIiÞ ¼ fbIj

1; bIj2; . . .g;

� DI�dhði : CÞðaÞ ffl ai, if Ii � hCðaÞ ffl ai, i.e., CIiðaIiÞ ffl a;

� DI�dhði : RÞða; bÞ ffl ai, if Ii � hRða; bÞ ffl ai, i.e., RIiðaIi; bIiÞ ffl a;

� DI�dFAi, iff DI�dp for every fuzzy assertion p ¼ hCðaÞ ffl ai;hRða; bÞ ffl ai in FAi;

� DI�dDFA if, for every i 2 IN; DI�dFAi, and DI d-satisfies everyindividual correspondence in IC.

Finally, DFA�dhði : CÞðaÞ ffl ai (read as ‘‘DFT d-entails hði : CÞðaÞffl ai”) if, for every distributed fuzzy interpretation DI; DI�dDFA im-plies DI�dhði : CÞðaÞ ffl ai. Similarly for hði : RÞða; bÞ ffl ai. We say DFAis satisfiable if there exists a DI such that DI�dDFA.

Now we give the semantics of DFR.A distributed fuzzy interpretation DI d-satisfies the elements of

a distributed fuzzy RBox DFR ¼ fFRigi2IN according to the followingclauses: for every i 2 IN,

� DI�dhi : R1 . . . Rm v R ffl ai, if Ii � hR1 . . . Rm v R ffl ai, i.e.,supa1 ;...;anþ1

ððRIi1ða1; a2Þ � . . .� RIi

nðan; anþ1ÞÞ ) RIiða1; anþ1ÞÞ ffl a;� DI�dtransði : RÞ, if Ii � transðRÞ, i.e., 8a; b 2 DIi; RIiða; bÞP

supc2DIi ðRIiða; cÞ � RIiðc; bÞÞ;� DI�ddisðði : R1Þ; ði : R2ÞÞ, if Ii � disðR1; R2Þ, i.e., 8a; b 2 DIi; RIi

1ða;bÞ ¼ 0 or RIi

2ða; bÞ ¼ 0;� DI�dref ði : RÞ, if Ii � ref ðRÞ, i.e., 8a 2 DIi; RIiða; aÞ ¼ 1;� DI�dirrði : RÞ, if Ii � irrðRÞ, i.e., 8a 2 DIi; RIiða; aÞ ¼ 0;� DI�dsymði : RÞ, if Ii � symðRÞ, i.e., 8a; b 2 DIi; RIiða; bÞ ¼ RIiðb; aÞ;� DI�dasyði : RÞ, if Ii � asyðRÞ, i.e., 8a; b 2 DIi, if RIiða; bÞ > 0 then

RIiðb; aÞ ¼ 0;� DI�dFRi, iff DI�dp for every fuzzy axiom p ¼ hR1 . . . Rm v R ffl ai;

transðRÞ; disðR1; R2Þ; ref ðRÞ; irrðRÞ; symðRÞ, or asy(R) in FRi;� DI�dDFR if, for every i 2 IN; DI�d FRi.

Finally, we provide the semantics of DFKB ¼ hDFR;DFT;DFAi.

Y. Jiang et al. / Expert Systems with Applications 37 (2010) 6052–6060 6055

A distributed fuzzy interpretation DI d-satisfies the DFKB ¼hDFR;DFT;DFAi (written as DI�dDFKB), iff DI�dDFR; DI�dDFT , andDI�dDFA. DFKB�dhi : C v D ffl ai (read as ‘‘DFKB d-entails hi : C vD ffl ai”) if, for every distributed fuzzy interpretationDI;DI�dDFKB implies DI�dhi : C v D ffl ai. Similarly forhði : CÞðaÞ ffl ai; hði : RÞða; bÞ ffl ai; hR1 . . . Rm v R ffl ai; transðRÞ; disðR1; R2Þ; ref ðRÞ; irrðRÞ; symðRÞ, and asy(R). We say DFKB is satisfi-able if there exists a DI such that DI�dDFKB. Concept i:C is satisfiablew.r.t. DFKB if there is a DI such that DI�dDFKB, and there is somea 2 DIi such that CIiðaÞ ¼ a, and a 2 (0,1].

In the following, we present the definition of distributed fuzzyontologies.

Distributed fuzzy ontologies: Formally, a distributed fuzzy ontol-ogy is a triple DFO ¼ hDFR; DFT; DFAi, where DFR is a distributedfuzzy RBox, DFT is a distributed fuzzy TBox, and DFA is a distrib-uted fuzzy ABox. Obviously, a distributed fuzzy ontology is in facta distributed fuzzy knowledge base of DFDLs from the DLs point ofview. For example, we can obtain the DFDL DFSROIQ(D), which isthe distributed extension of fuzzy DL FSROIQ(D) (Bobillo, 2008; Bo-billo et al., 2009). On the other hand, from the ontology point ofview, distributed fuzzy ontologies are the integration between dis-tributed ontologies (Bouquet, Giunchiglia, Harmelen, Serafini, &Stuckenschmidt, 2004; Maedche, Motik, & Stojanovic, 2003) andfuzzy ontologies (Tho et al., 2006; Tho, Hui, Fong & Cao, 2006), orare the distributed extensions of fuzzy ontologies.

3. Distributed fuzzy context-domain relevance model

In the current section, we will present the distributed fuzzycontext-domain relevance (DFCDR) model, which is the distributedfuzzy extension of the CDR model (Bobillo et al., 2008). This in-cludes the representation, reasoning, and implementation of theDFCDR model.

3.1. Representation

Before defining the DFCDR model, let us define two (distrib-uted) fuzzy ontological knowledge submodels: the distributed fuz-zy domain ontologies and the fuzzy context ontology.

The distributed fuzzy domain ontology DFOD ¼ h DFRD;

DFTD; DFADi contains the knowledge required to solve the con-crete problem that the system is facing, where DFRD ¼ fFRD

i gi2IN;

DFTD ¼ hfFTDi gi2IN ; fFBD

ijgi–j2INi, and DFAD ¼ hfFADi gi2IN ; fIC

Dijgi–j2INi.

In what follows, let DFODi ¼ hFRD

i ; FTDi ; FAD

i i, in other words, DFODi

is the i-th fuzzy domain ontology of DFOD. As expected, conceptsof this distributed fuzzy domain ontology represent entities withassociated semantics, roles establish the weighted connectionsamong them, instances represent individuals of this word, fuzzybridge rules set up the weighted relevance relations between con-cepts of different fuzzy domain ontologies, and individual corre-spondences establish the correspondences between individuals ofdifferent fuzzy domain ontologies. This distributed fuzzy domainontologies can be arbitrarily complex and are closely related tothe problem. We will use the notation i : D 2 DFOD

i to name com-plex concept expressions i:D built using elements in DFOD

i andontology constructs. Note that, in principle, these i:D are not partof the distributed fuzzy domain ontologies.

The fuzzy context ontology FOC ¼ hFRC ; FTC ; FACi contains theknowledge required to express the circumstances or the surround-ings under which the domain knowledge will be used, where FRC isa fuzzy RBox, FT is a fuzzy TBox, and FA is a fuzzy ABox. It is thesame as that of the context ontology (Bobillo et al., 2008), the fuzzycontext ontology can be seen as a (formal) vocabulary with whichthese situations can be described. Being strict, context knowledgeis not part of the original problem, though it can be indispensable

to solve it; in fact, it would be possible to reuse the same contextmodel in completely different areas. Fuzzy context knowledgecan range from low-level sensor data (like location, time, orhumidity) to abstract information (like preferences, desires, ormental states). We will use the notation C 2 FOC to name complexconcept expressions C built using elements in FOC and ontologyconstructs. Like in the previous case, these C are not necessarilypart of the fuzzy context ontology.

Obviously, the distributed fuzzy domain ontologies and fuzzycontext ontology are the extensions of domain ontology and con-text ontology (Bobillo et al., 2008), respectively.

Now we provide the definition of the DFCDR model.It is similar to the CDR ontology (Bobillo et al., 2008), the DFCDR

ontology is made of new classes (the so-called fuzzy profiles) thatwill relate C context concepts with i:D domain concepts throughquantified roles. With the same as the CDR ontology, our proposal(DFCDR model) only considers the intensional component of thedistributed fuzzy knowledge base, in other words, we only con-sider the distributed fuzzy TBox and distributed fuzzy RBox, anddo not consider the distributed fuzzy ABox.

Definition 1. Let DFOD ¼ hDFRD; DFTDi and FOC ¼ hFRC ; FTCi be,respectively, the distributed fuzzy domain ontologies and fuzzycontext ontology, where DFRD ¼ fFRD

i gi2IN and DFTD ¼ hfFTDi gi2IN ;

fFBDijgi–j2INi; DFOD

j ¼ hFRDj ; FTD

j i an arbitrary but fixed fuzzy ontol-ogy of DFOD; Ci 2 FOC a context concept built using elements inFOC and ontology constructs, and j : Dj 2 DFOD

j a domain conceptbuilt using elements in DFOD

j and ontology constructs.

The DFCDR ontology that relates the set of pairs of conceptsfðCi; j : DjÞg (i.e., states that j : Dj is interesting to some extentwhen Ci happens) is a fuzzy ontology FOP ¼ hFRP; FTPi thatsatisfies:

(1) FTP includes definitions for concepts P>; C>; D>; Pi;j; Ci, andj : Dj, where

(a) P>; C>, and j : D> are the super-class Profile, Context,

and Domain:hPi;j v P> P 1i ^ hP> v ti;jPi;j P 1i ^ hti;jPi;j v P> P 1i;hCi v C> P 1i ^ hC> v tiCi P 1i ^ htiCi v C> P 1i;hj : Dj v j : D> P 1i ^ hj : D> v tjj : Dj P 1i ^ htjj : Dj v j :

D> P 1i;(b) R1 is the fuzzy bridge property linking fuzzy profiles

and context concepts:hP> v 8R1:C> P 1i;(c) R2 is the fuzzy bridge property linking fuzzy profiles

and domain concepts:hP> v 8R2:j : D> P 1i;

(d) Pi;j is the fuzzy profile linking named context Ci andnamed domain j : Dj:

hPi;j v ð9R1:Ci u 9R2:j : DjÞP ai;ji ^ hð9R1:Ci u 9R2:j : DjÞ vPi;j P ai;ji, where ai, j 2 (0,1];

(2) FTP ¼ fR1;R2g;(3) FOP is consistent.

Fig. 1 depicts the meaning of this definition. It shows how Pi;j

concepts are a reification of the notion of ‘‘weighted relevance”relationship between context and domain concepts.

3.2. Reasoning

The main reasoning task within the DFCDR ontology will be tofind the distributed fuzzy domain knowledge restricted by a fuzzycontext, that is, to find all the classes of the distributed fuzzy do-main ontologies that are associated using fuzzy profiles (i.e., areweighted relevant) with a given concept built with the contextvocabulary. Since distributed fuzzy domain ontologies consist of

Fig. 1. A sample of distributed fuzzy context-domain relevance ontology.

6056 Y. Jiang et al. / Expert Systems with Applications 37 (2010) 6052–6060

fuzzy ontologies and the corresponding fuzzy bridge rules betweenthese fuzzy ontologies, therefore, to find all the classes of the dis-tributed fuzzy domain ontologies that are weighted relevant tothe context concepts, we have to translate the distributed fuzzydomain ontologies into a ‘‘global” fuzzy domain ontology firstly.That is to say, we will do so by building a ‘‘global” fuzzy domainontology, which encodes the knowledge available in the (local) fuz-zy ontologies and the fuzzy bridge rules of the distributed fuzzydomain ontologies. In the following, we present the translation ap-proach formally.

Since distributed fuzzy ontologies are the extensions of distrib-uted ontologies (or distributed DLs), hence, the translation ap-proach which we define here can be obtained through extendingthe translation from distributed DLs (DDLs) to DLs (Borgida & Ser-afini, 2003; Serafini et al., 2005).

To do so, we start by creating a fuzzy domain ontology (or lan-guage), GFOD ¼ hGFRD; GFTDi (or GFDL), for descriptions in this glo-bal FDL. Suppose one is given a family of fuzzy ontologies (or fuzzyDLs) fDFOD

i gi2IN (or fFDLDi gi2INÞ. For any primitive concept A (resp.,

role R) of DFODi , let i:A (resp., i:R) be a primitive concept (resp., role)

of GFOD. Moreover, GFOD will use all the concept and role construc-tors appearing in any DFOD

i . Therefore, GFOD permits the equiva-lents of at least all composite descriptions of DFOD

i . GFOD has theusual top and bottom concepts, > and ?, which in this case are dis-tinguished from the tops and bottoms of the hierarchies in DFOD

i ,which are now ordinary concepts, with names i : > and i :?. (Toemphasize this, we will use instead the symbols >i and ?i.) GFOD

has a special set of role symbols Rij, which will be used to simulatethe domain relations, as well as an additional role symbol P*, usedstrictly for technical reasons.

We start by providing a translation #() from DFODi concepts/

roles to concepts/roles in the GFOD, and then extending it to mapentire GFOD (i.e., GFRD and GFTDÞ. Not unexpectedly, such a transla-tion will be used on the recursive structure of concepts, which isbased on the use of FDL (or DL) constructors. To emphasize this,we will view concepts and role constructors as functors, q,that take as arguments simpler descriptions. For example, 8R. Ccan be viewed as all(R, D), where allðhrole expressioni;hconcept expressioniÞ is the constructor functor. In fact, this nota-tion is the same as that of the translation from DDLs to DLs (Borg-ida & Serafini, 2003; Serafini et al., 2005). The mapping # is definedrecursively as follows:

1. #(i, M) = i:M for atomic concepts and roles M (including M = >and ?);

2. if q is a concept constructor taking k arguments, then#ði;qðM1; . . . ;MkÞÞ ¼ >i u qð#ði;M1Þ; . . . ;#ði;MkÞÞ;

3. if q is a role constructor taking k arguments, then#ði;qðM1; . . . ;MkÞÞ ¼ qð#ði;M1Þ; . . . ;#ði;MkÞÞ.

We are now ready to construct the GFTD of GFOD.

Definition 2. Applying # to a DFTD ¼ hfFTDi gi2IN ; fFBD

ijgi – j2INiyields a GFTD #ðDFTDÞ of GFOD consisting of the following axioms:

1. h#ði; CÞ v #ði;DÞ ffl ai for all hi : C v D ffl ai 2 FTDi ;

2. h#ði; CÞ v 8Rij:#ðj;DÞ . ai for every fuzzy positive into-bridge rule hi : C!v j : D . ai 2 FBD

ij ;3. h#ðj;DÞ v 9Rij :#ði;CÞ . ai for every fuzzy positive onto-

bridge rule hi : C!w j : D . ai 2 FBDij ;

4. h#ði; CÞ v 8Rij:#ðj;DÞ / ai for every fuzzy negative into-bridge rule hi : C!v j : D / ai 2 FBD

ij ;5. h#ðj;DÞ v 9Rij :#ði;CÞ / ai for every fuzzy negative onto-

bridge rule hi : C!w j : D / ai 2 FBDij ;

6. h?i v?P 1i;7. hi : A v >i P 1i for every atomic concept A of DFOD

i ;8. h> v 9P�:>i P 1i;9. h>i v 8ði : RÞ:>i P 1i for every role R of DFOD

i ;10. h9ði : RÞ:> v >i P 1i for every role R of DFOD

i .

Now we construct the GFRD of GFOD.

Definition 3. Applying # to a DFRD ¼ fFRDi gi2IN , yields a

GFRD#ðDFRDÞ of GFOD, consisting of the following axioms:

1. h#ði;R1 . . . RmÞ v #ði;RÞ ffl ai for all hi : R1 . . . Rm v R ffl ai 2 FRDi ;

2. disð#ði;R1Þ;#ði;R2ÞÞ for every disðði : R1Þ; ði : R2ÞÞ 2 FRDi ;

3. trans(#(i, R)) for every transði : RÞ 2 FRDi ;

4. ref(#(i, R)) for every ref ði : RÞ 2 FRDi ;

5. irr(#(i, R)) for every irrði : RÞ 2 FRDi ;

6. sym(#(i, R)) for every symði : RÞ 2 FRDi ;

7. asy(#(i, R)) for every asyði : RÞ 2 FRDi .

Obviously, we can construct the GFOD through the translation#(), i.e., GFOD ¼ #ðDFODÞ ¼ h#ðDFRDÞ;#ðDFTDÞi ¼ h#ðfFRD

i gi2INÞ;#ðfFTD

i gi2INÞ [#ðfFBDijgi – j2INÞi ¼ hGFRD; GFTDi.

Based on the global fuzzy domain ontology GFOD that is ob-tained from the distributed fuzzy domain ontologies DFOD ¼hGFRD; GFTDi through the translation #(), we can define the mainreasoning task within the DFCDR ontology. That is, to find all theclasses of the distributed fuzzy domain ontologies that are associ-ated using fuzzy profiles with a given concept built with the con-text vocabulary can be expressed as follows:

Y. Jiang et al. / Expert Systems with Applications 37 (2010) 6052–6060 6057

Definition 4. Given DFOD ¼ hDFRD; DFTDi; FOC ¼ hFRC ; FTCi, andFOP ¼ h FRP ; FTPi. GFOD ¼ hGFRD; GFTDi is the global fuzzy domainontology obtained from DFOD; DFOD

j ¼ hFRDj ; FTD

j i. The restrictedfuzzy domain of the scenario S 2 FOC (being S a complex conceptexpressed in FTC vocabulary) considering FOP comprises all theclasses I such asfI 2 GFTDjðhS v Cn P aiÞ ^ ðPn;m 2 FTPÞ ^ ðhI v j : Dm P ai_

ðhI v i : Dk P ai ^ hj : Dm v i : Dk P ai ^ hi : Dk v j : Dm P aiÞÞg,where Cn 2 FTC ; j : Dm 2 FTD

j ; i : Dk 2 GFTD; i; j 2 IN; i – j, anda 2 (0,1].

Intuitively, we first find the classes fCng of FTC that satisfy thecondition hS v Cn P ai, and then find the classes {I} of FTD

j that sat-isfy the condition hI v j : Dm P ai through the DFCDR ontology (seeFig. 1). Since there exists other fuzzy domain ontologies besidesDFOD

j , hence, we also need to find the classes {I} of these remainingfuzzy domain ontologies that are a-equivalent to the j : Dm, i.e., theclasses {I} that satisfy the condition hI v i : Dk P ai ^ hj : Dm vi : Dk P ai ^ hi : Dk v j : Dm P ai, where i–j.

Formally, we can present the algorithm of finding the classes {I}of global fuzzy domain ontology (or distributed fuzzy domainontologies) as follows. This algorithm is the extension of Algorithm1 of (Bobillo et al., 2008).

Algorithm 1. Finding the restricted domain of a scenario Sconsidering FOP under distributed fuzzy domain ontologies DFOD

Input: a scenario S, distributed fuzzy domain ontologies DFOD,and a 2 (0,1]Output: the restricted domain of a scenario SSteps:(1) Translate the DFOD into a global fuzzy domain ontology

GFOD using the translation #().(2) Retrieve all the named contexts Cn that approximate sub-

sumes S, and the subsumption degree between conceptCn and concept S is at least a:

fCn 2 FTC jhCn v C> P 1i ^ hS v Cn P aig:

(3) Retrieve all the named profiles Pk;l that approximateinclude Cn contexts (via R1):

fPk;l 2 FTP jhPk;l v P> P 1i ^ hPk;l v 9R1:Ck P ai ^ hCn v Ck

P aig:

(4) Retrieve all the named domains j : Dm that are approxi-mate related to Pk;l profiles (via R2):

fj : Dm 2 FTDj jhj : Dm v >j P 1i ^ hPk;l v 9R2:j : Dm P aig:

(5) Retrieve all the named domains i : Dh that are a-equiva-lent to the j : Dm:

fi : Dh 2 GFTDjhj : Dm v i : Dh P ai ^ hi : Dh v j : Dm

P ai ^ i–jg:

(6) Retrieve all the classes I from GFTD that are approximatesubsumed by j : Dm or i : Dh:

fI 2 GFTDjhI v j : Dm P ai _ hI v i : Dh P aig:

Computational complexity of the reasoning within the DFCDRmodel is conditioned by complexity of context and domain expres-sions ðCn 2 FTC and j : Dm; i : Dh 2 GFTDÞ, since Pk;l definitions areincluded in FALC (fuzzy ALC) (Straccia, 2001) level. It is obvious toknow that translating the DFOD into GFOD can be carried out inpolynomial time from the definition of the translation #(). Conse-

quently, in the simplest case, that is, FOC ; DFOD (or GFODÞ, andFOP ontologies are constructed using FALC with simple and acyclicTBoxes, reasoning within the DFCDR model under Zadeh semanticsis PSPACE-complete (Straccia, 2001). Obviously, we may constructDFOD and FOC using other fuzzy DLs other than FALC such as FSHIN(Stoilos et al., 2007) and FSROIQ (or FSROIQ(D)) (Bobillo, 2008; Bo-billo et al., 2009). If we adopt the fuzzy DL FSHIN, reasoning withinthe DFCDR model under Zadeh semantics is 2-NEXPTIME (Stoiloset al., 2007). Regarding the FSROIQ and FSROIQ(D), they are the cur-rent newest fuzzy DLs, and the FSROIQ(D) has the most expressivepower in all fuzzy DLs currently. If we adopt the FSROIQ, reasoningwithin the DFCDR model under Gödel semantics is OðjTVjkÞ,where TV is a finite set of the degrees of truth, k is the maximaldepth of universal restriction concepts appearing (Bobillo et al.,2009). Certainly, it is possible to reduce the complexity of theDFCDR model by restricting the allowed constructors for DFOD

and FOC , moving consequently to a less expressive logic. For in-stance, restricting negation to atomic concepts and disallowing un-ion concepts would enclose the DFCDR ontology to fuzzy DL FALe,which has PSPACE complexity for general reasoning (i.e., with Gen-eral Concept Inclusion, GCIs). Other alternative consists on usingonly acyclic TBoxes, which would give complexities of PSPACEfor FALC and coNP for FALe. Since the reasoning of FALC and FALecan be reduced to the reasoning of ALC and ALe, respectively, byproviding reasoning preserving procedure to obtain a crisp repre-sentation for them under Zadeh semantics and Gödel semantics,here, the reasoning complexity of FALC and FALe is the same as thatof ALC and ALe, respectively.

3.3. Implementation

From Algorithm 1, we know that the reasoning within theDFCDR model can be translated into the reasoning of fuzzy DLs.Therefore, we can implement the reasoning within the DFCDRmodel by using the existing fuzzy DLs reasoning systems.

It is well known that different families of fuzzy operators lead todifferent fuzzy DLs. In fuzzy logic, there are three main families offuzzy operators: Lukasiewicz, Gödel, and product (Bobillo et al.,2009). The mainly related reasoning systems about fuzzy DLs areas follows.

The oldest fuzzy DLs reasoning system is fuzzyDL (Bobillo &Straccia, 2008), which extends fuzzy DL FSHIF(D) with conceptmodifiers, explicit definitions of fuzzy concepts, concrete featuresor datatypes. Moreover, fuzzyDL supports both Zadeh and Lukasie-wicz families of fuzzy operators. Consequently, we can use thefuzzyDL system to implement the reasoning within the DFCDRmodel that is constructed in the fuzzy DL FSHIF(D) under Zadehsemantics and Lukasiewicz semantics, where FSHIF(D) is a fuzzyextension of SHIF(D) (equivalent to OWL Lite).

FIRE (Stoilos, Simou, Stamou, & Kollias, 2006) implements thetableau algorithm for fuzzy DL FSHIN described in (Stoilos et al.,2007). It restricts itself to the Zadeh family. Therefore, we canuse the FIRE system to implement the reasoning within the DFCDRmodel that is constructed in the fuzzy DL FSHIF under Zadehsemantics.

GERDS (Habiballa, 2007) implements a resolution algorithm forfuzzy DL FALC with role negation, top role, and bottom role underLukasiewicz family. Hence, we can use the GERDS system to imple-ment the reasoning within the DFCDR model that is constructed inthe fuzzy DL FALC under Lukasiewicz semantics.

KAON2 (http://kaon2.semanticweb.org/) implements thereduction of fuzzy DLs to crisp DLs presented by Straccia (2004).Concretely, Straccia presented a reasoning preserving transforma-tion of FALCH into classical ALCH under Zadeh semantics, wheregeneral terminological axioms are allowed. Consequently, we canuse the KAON2 system to implement the reasoning within the

Fuzzy context ontology

Distributed fuzzy context-domain

relevance ontology

Global fuzzy domain ontology

Distributed fuzzy domain ontologies

Fuzzy DL reasoner

Fuzzy scenario model (Client)

Fig. 2. Architecture of the DFCDR model reasoning system.

6058 Y. Jiang et al. / Expert Systems with Applications 37 (2010) 6052–6060

DFCDR model that is constructed in the fuzzy DL FALCH under Za-deh semantics.

DeLorean (DEscription LOgic REasoner with vAgueNess) (Bobil-lo, Delgado, & Gomez-Romero, 2008) is the first reasoner that sup-ports fuzzy extensions of the language OWL and OWL 2. It reducesreasoning in fuzzy DL FSROIQ(D) under Zadeh or Gödel family toreasoning in crisp SROIQ(D). Given a fuzzy ontology in the exten-sion of OWL or OWL 2 (Bobillo, 2008), DeLorean computes its crisprepresentation in OWL or OWL 2, respectively. In a strict sense,DeLorean is not a reasoner but a translator from a fuzzy ontologylanguage to a classical ontology language (the standard languageOWL or OWL 2, depending on the expressivity of the original ontol-ogy). Then, a classical DL reasoner is employed to reason with theresulting ontology. But due to this ability of combining the reduc-tion procedure with the crisp reasoning, DeLorean is referred to asa reasoner. In the current version, DeLorean supports the fuzzy DLFSROIQ(D) under Zadeh semantics and Gödel semantics. Therefore,we can use the DeLorean system to implement the reasoning with-in the DFCDR model that is constructed in the fuzzy DL FSROIQ(D)under Zadeh semantics and Gödel semantics.

Fig. 2 illustrates the architecture of the reasoning within theDFCDR model.

There is a remark here. In practical applications, a suitableknowledge model that describes semantically the informationto be managed need to be constructed following the DFCDR pat-tern, hence, firstly we have to build three kinds of ontologieswhich, respectively, characterize the information about the do-main knowledge (distributed fuzzy domain ontologies), define aontology to describe the context situation (fuzzy context ontol-ogy), and connect subsets of both of domain knowledge and ofcontext situation (fuzzy relevance ontology). Regarding the do-main ontologies (including the fuzzy bridge rules among domainontologies), we may construct them in advance. However,although we cannot completely built the fuzzy context ontologyand the fuzzy relevance ontology in advance, we may constructthe vocabulary to describe the situation and the relevance modelbeforehand in order to meet the special requirements of the mo-bile systems such as the emergency of a outdoors healthcaresystem.

4. Related work

Nowadays, advent of new portable devices and wireless com-munication technologies has resulted in putting more emphasisin mobile applications, given raise to the so-called area of perva-sive computing. Pervasive computing aims to develop technologies

that support every day routines unobtrusively using a swarm of re-duced wireless-connected computing devices (Bobillo et al., 2008;Weiser, 1999). To provide adequate services for the users, applica-tions and services should be aware of their contexts and automat-ically adapt to their changing contexts known as context-awareness (Bolchini et al., 2007; Feng et al., 2009; Hong et al.,2009; Kang et al., 2008; Kim et al., 2009). In other words, con-text-awareness, defined as the capacity to acquire, representsand processes context information to change application behavior,has been traditionally remarked as a key requisite for pervasivesystems (Satyanarayanan, 2001).

A highly descriptive formalism with reasoning features is con-venient for context-knowledge representation and management.Not surprisingly, ontologies have been proposed to be used formodeling context knowledge, as they provide some advantagesover other formalisms: reusability, sharing, reasoning, standardi-zation, supporting tools, etc. (Bobillo et al., 2008; Weiser, 1999;Strang & Linnhoff-Popien, 2004). Some approaches are for in-stance these in (Cai, Hu, Lü, & Cao, 2009; Chen, Finin, & Joshi,2005; Kwon & Kim, 2009; Lee, Seo, & Rhee, 2008; Yang, Zhang,& Chen, 2008). It is worth to note that most of these works bor-row technologies from the Semantic Web (Berners-Lee, Hendler,& Lassila, 2001). Actually, skyrocketing research activity in theSemantic Web during last years has contributed with several the-ories and tools that have been assimilated by Pervasive comput-ing. For instance, in (Ranganathan, McGrath, Campbell, &Mickunas, 2003), some issues that can be addressed using theSemantic Web technologies are explained. (Masuoka, Labrou, Par-sia, & Sirin, 2003) tackles one of these problems, the automaticcoordination of actors in mobile interaction and suggests attach-ing formal descriptions to services in order to discover, communi-cate, and integrate clients and providers in pervasiveenvironments. It is well known that properties and semantics ofontology constructs in the Semantic Web mainly are determinedby DLs (Baader et al., 2007; Horrocks, 2008). Concretely, theSemantic Web consists of several hierarchical layers, where theontology layer, in the form of the OWL Web Ontology Language(recommended by the W3C), is currently the highest layer of suf-ficient maturity (Horrocks, Patel-Schneider, & Harmelen, 2003).Nowadays, the up to date version of the Web Ontology Languageis OWL 2 (Grau et al., 2008). In fact, OWL 2 has a formal seman-tics and a reasoning support through a mapping to the DLSROIQ(D) (Bobillo, 2008; Horrocks et al., 2006). That is to say,OWL 2 is equivalent to the DL SROIQ(D) theoretically. However,these OWLs (or DLs) are inadequate to model decentralizationand become less suitable in distributed domains in which theconcepts to be represent come from multiple ontologies (orknowledge bases). In this aspect, (Bouquet et al., 2004) proposesC-OWL, an extension to OWL to define mappings between locallyinterpreted and globally valid ontologies. In theory, (Borgida &Serafini, 2003; Serafini et al., 2005) presents distributed descrip-tion logics.

Recently, Bobillo et al. (2008) presented a proposal to tackle theproblem of information overload, paying special attention to mo-bile KBSs, by using context knowledge. The core of the approachis the context-domain relevance (CDR) model; however, the CDRmodel cannot deal with fuzzy information and multiple distributeddomain ontologies. The work described in this paper is a distrib-uted fuzzy extension of the CDR model, i.e., the distributed fuzzycontext-domain relevance (DFCDR) model is provided.

5. Conclusion

In this work, we present the DFCDR model, which is a distrib-uted fuzzy extension of the CDR model. This model allows to cope

Y. Jiang et al. / Expert Systems with Applications 37 (2010) 6052–6060 6059

with the problem of information overload in distributed fuzzyKBSs, which is critical in mobile systems due to their special fea-tures. Besides the model, we also provide a reasoning procedureto infer which sections of the distributed fuzzy domain knowledgeare interesting or significant in a given situation. Furthermore, wegive the implementation approach of the DFCDR model reasoningsystem by using the existing fuzzy DLs reasoning systems.

Current research effort is to implement the DFCDR model rea-soning system and to perform an empirical evaluation in real sce-narios. An interesting topic of future research is to study theprobabilistic, possibilistic, or rough generalizations of the CDRmodel based on probabilistic DLs (Lukasiewicz, 2008), possibilisticDLs (Hollunder, 1995), or rough DLs (Jiang, Tang, Wang, & Tang,2009; Jiang, Wang, Deng, & Tang, 2009; Jiang, Wang, Tang, & Xiao,2009), respectively.

Acknowledgements

The works described in this paper are supported by the NationalNatural Science Foundation of China under Grant Nos. 60663001,60673135, 60970044; The Natural Science Foundation of GuangxiProvince of China under Grant Nos. 0991100, 0832103; The Foun-dation of the State Key Laboratory of Computer Science of ChineseAcademy of Sciences under Grant No. SYSKF0904; and The ScienceResearch and Technology Development Project of Guangxi Prov-ince of China under Grant No. 0719001-11.

References

Baader, F., Calvanese, D., McGuinness, D., Nardi, D., & Patel-Schneider, P. F. (2007).The description logic handbook: Theory (2nd ed.). Cambridge University Press.

Berners-Lee, T., Hendler, J., & Lassila, O. (2001). The Semantic Web. ScientificAmerican, 284(5), 34–43.

Bobillo, F. (2008). managing vagueness in ontologies. PhD Dissertation. Spain:University of Granada.

Bobillo, F., & Straccia, U. (2008). fuzzyDL: An expressive fuzzy description logicreasoner. In Proceedings of the 17th IEEE international conference on fuzzy systems(FUZZ-IEEE 2008) (pp. 923–930).

Bobillo, F., Delgado, M., & Gomez-Romero, J. (2008). Representation of context-dependant knowledge in ontologies: A model and an application. Expert Systemswith Applications, 35(4), 1899–1908.

Bobillo, F., Delgado, M., Gomez-Romero, J., & Straccia, U. (2009). Fuzzy descriptionlogics under Gödel semantics. International Journal of Approximate Reasoning,50(3), 494–514.

Bobillo, F., Delgado, M., & Gomez-Romero, J. (2008). DeLorean: A reasoner for fuzzyOWL 1.1. In Proceedings of the 4th international workshop on uncertaintyreasoning for the Semantic Web (URSW 2008).

Bolchini, C., Schreiber, F. A., & Tanca, L. (2007). A methodology for a very small database design. Information Systems, 32(1), 61–82.

Borgida, A., & Serafini, L. (2003). Distributed description logics: Assimilatinginformation from peer sources. Journal of Data Semantics, 1(1), 153–184.

Bouquet, P., Giunchiglia, F., Harmelen, F., Serafini, L., & Stuckenschmidt, H. (2004).Contextualizing ontologies. Journal of Web Semantics, 1(4), 325–343.

Byun, H. E., & Cheverst, K. (2004). Utilizing context history to provide dynamicadaptations. Applied Artificial Intelligence, 18(6), 533–548.

Cai, H., Hu, X., Lü, Q., & Cao, Q. (2009). A novel intelligent service selection algorithmand application for ubiquitous web services environment. Expert Systems withApplications, 36(2), 2200–2212.

Chen, H., Finin, T., & Joshi, A. (2005). The SOUPA ontology for pervasive computing.Ontologies for agents: Theory and experiences. Whitestein series in software agenttechnologies. Springer.

Dey, A. K. (2001). Understanding and using context. Personal and UbiquitousComputing, 5(1), 4–7.

Eppler, M., & Mengis, J. (2004). The concept of information overload: A review ofliterature from organization science, accounting, marketing, MIS, and relateddisciplines. The Information Society, 20(5), 325–344.

Farhoomand, A. F., & Drury, D. H. (2002). Managerial information overload.Communications of the ACM, 45(10), 127–131.

Fendel, D. (2001). Ontologies: A silver bullet for knowledge management and electroniccommerce. Springer-Verlag.

Feng, Y. H., Teng, T. H., & Tan, A. H. (2009). Modelling situation awareness forcontext-aware decision support. Expert Systems with Applications, 36(1),455–463.

Ghidini, C., & Giunchiglia, F. (2001). Local model semantics, or contextualreasoning = locality + compatibility. Artificial Intelligence, 127(2), 221–259.

Grau, B. C., Horrocks, I., Motik, B., Parsia, B., Patel-Schneider, P., & Sattler, U. (2008).OWL 2: The next step for OWL. Journal of Web Semantics, 6(4), 309–322.

Grau, B. C., Parsia, B., & Sirin, E. (2006). Combining OWL ontologies using e-connections. Journal of Web Semantics, 4(1), 40–59.

Habiballa, H. (2007). Resolution strategies for fuzzy description logic. In Proceedingsof the 5th conference of the european society for fuzzy logic and technology(EUSFLAT 2007) (pp. 27–36).

Hajek, P. (1998). Metamathematics of fuzzy logic. Kluwer Academic Publishers.Hollunder, B. (1995). An alternative proof method for possibilistic logic and its

application to terminological logics. International Journal of ApproximateReasoning, 12(2), 85–109.

Hong, J., Suh, E., & Kim, S. (2009). Context-aware systems: A literature review andclassification. Expert Systems with Applications, 36(4), 8509–8522.

Hong, J., Suh, E., Kim, J., & Kim, S. (2009). Context-aware system for proactivepersonalized service based on context history. Expert Systems with Applications,36(4), 7448–7457.

Horrocks, I. (2008). Ontologies and the Semantic Web. Communications of the ACM,51(12), 58–67.

Horrocks, I., Kutz, O., & Sattler, U. (2006). The even more irresistible SROIQ. InProceedings of the 10th international conference of knowledge representation andreasoning (KR 2006) (pp. 57–67).

Horrocks, I., Patel-Schneider, P. F., & Harmelen, F. V. (2003). From SHIQ and RDF to OWL:The making of a Web ontology language. Journal of Web Semantics, 1(1), 7–26.

Jiang, Y., Tang, Y., Wang, J., & Tang, S. (2009). Reasoning within intitutionistic fuzzyrough description logics. Information Sciences, 179(14), 2362–2378.

Jiang, Y., Wang, J., Deng, P., & Tang, S. (2009). Reasoning within expressive fuzzyrough description logics. Fuzzy Sets and Systems, 160(23), 3403–3424.

Jiang, Y., Wang, J., Tang, S., & Xiao, B. (2009). Reasoning with rough descriptionlogics: An approximate concepts approach. Information Sciences, 179(5),600–612.

Kang, H., Suh, E., & Yoo, K. (2008). Packet-based context aware system to determineinformation system user’s context. Expert Systems with Applications, 35(1–2),286–300.

Kim, N., Lee, H. S., Oh, K. J., & Choi, J. Y. (2009). Context-aware mobile service forrouting the fastest subway path. Expert Systems with Applications, 36(2),3319–3326.

Kutz, O., Lutz, C., Wolter, F., & Zakharyaschev, M. (2004). e-connections of abstractdescription systems. Artificial Intelligence, 156(1), 1–73.

Kwon, O. (2009). A social network approach to resolving group-level conflict incontext-aware services. Expert Systems with Applications, 36(5), 8967–8974.

Kwon, O., & Kim, J. (2009). Concept lattices for visualizing and generating userprofiles for context-aware service recommendations. Expert Systems withApplications, 36(2), 1893–1902.

Lee, J. Y., Seo, D. W., & Rhee, G. (2008). Visualization and interaction of pervasiveservices using context-aware augmented reality. Expert Systems withApplications, 35(4), 1873–1882.

Li, Y., Xu, B., Lu, J., & Kang, D. (2006). A distributed and fuzzy extension ofdescription logics. Knowledge-based intelligent information and engineeringsystems. Lecture notes in computer science (Vol. 4251). Springer. pp. 655–662.

Lukasiewicz, T. (2008). Expressive probabilistic description logics. ArtificialIntelligence, 172(6–7), 852–883.

Lukasiewicz, T., & Straccia, U. (2008). Managing uncertainty and vagueness indescription logics for the Semantic Web. Journal of Web Semantics, 6(4),291–308.

Maedche, A., Motik, B., & Stojanovic, L. (2003). Managing multiple and distributedontologies on the Semantic Web. The VLDB Journal — The International Journal onVery Large Data Bases, 12(4), 286–302.

Masuoka, R., Labrou, Y., Parsia, B., & Sirin, E. (2003). Ontology-enabled pervasivecomputing applications. IEEE Intelligent Systems, 18(5), 68–72.

Ranganathan, A., McGrath, R. E., Campbell, R. H., & Mickunas, M. D. (2003). Use ofontologies in a pervasive computing environment. Knowledge EngineeringReview, 18(3), 209–220.

Satyanarayanan, M. (2001). Pervasive computing: Vision and challenges. IEEEPersonal Communications, 8(4), 10–17.

Serafini, L., Borgida, A., & Tamilin, A. (2005). Aspects of distributed and modularontology reasoning. In Proceedings of the 19th international joint conference onartificial intelligence (IJCAI 2005) (pp. 570–575).

Stoilos, G., Simou, N., Stamou, G., & Kollias, S. (2006). Uncertainty and the SemanticWeb. IEEE Intelligent Systems, 21(5), 84–87.

Stoilos, G., Stamou, G., Pan, J. Z., Tzouvaras, V., & Horrocks, I. (2007). Reasoning withvery expressive fuzzy description logics. Journal of Artificial Intelligence Research,30, 273–320.

Straccia, U. (2001). Reasoning within fuzzy description logics. Journal of ArtificialIntelligence Research, 14, 137–166.

Straccia, U. (2004). Transforming fuzzy description logics into classical descriptionlogics. In Proceedings of the 9th European Conference on Logics in ArtificialIntelligence (JELIA 2004) (pp. 385–399).

Straccia, U. (2006). A fuzzy description logic for the Semantic Web. In CapturingIntelligence: Fuzzy Logic and the Semantic Web (pp. 73–90). Elsevier SciencePublishers.

Strang, T. & Linnhoff-Popien, C. (2004). A context modeling survey. In Workshop onadvanced context modelling, reasoning and management associated with the sixthinternational conference on ubiquitous computing (UbiComp 2004).

Studer, R., Benjamins, V. R., & Fensel, D. (1998). Knowledge engineering: Principlesand methods. Data and Knowledge Engineering, 25(1–2), 161–197.

Tho, Q. T., Hui, S. C., & Fong, A. C. M. (2006). Automatic fuzzy ontology generation forsemantic help-desk support. IEEE Transactions on Industrial Informatics, 2(3),155–164.

6060 Y. Jiang et al. / Expert Systems with Applications 37 (2010) 6052–6060

Tho, Q. T., Hui, S. C., Fong, A. C. M., & Cao, T. H. (2006). Automatic fuzzy ontologygeneration for Semantic Web. IEEE Transactions on Knowledge and DataEngineering, 18(6), 842–856.

Weiser, M. (1999). The computer for the 21st century. Mobile Computing andCommunications Review, 3(3), 3–11.

Yang, S. J. H., Zhang, J., & Chen, I. Y. L. (2008). A JESS-enabled context elicitationsystem for providing context-aware Web services. Expert Systems withApplications, 34(4), 2254–2266.

Zhang, W., Yoshida, T., & Tang, X. (2009). Using ontology to improve precision ofterminology extraction from documents. Expert Systems with Applications, 36(5),9333–9339.

Zhou, B., Lu, J., Li, Y., Zhang, Y., & Kang, D. (2008). Reasoning problems on distributedfuzzy ontologies. Rough sets and knowledge technology. Lecture notes in computerscience (Vol. 5009). Springer. pp. 588–595.