International Journal of Computational Intelligence Systems, Vol. 5, No. 6 (November, 2012), 1089-1108 An Ontology as a Tool for Representing Fuzzy Data in Relational Databases Carmen Martinez-Cruz 1∗, Ignacio J. Blanco and M. Amparo Vila2 1 Computing Department, University of Jaen, Campus de las Lagunillas S/N, Jaen, 23071, Spain E-mail: [email protected] 2 Computation Science and A.I. Department, University of Granada Periodista Daniel Saucedo Aranda S/N, Granada, 18071, Spain E-mail: iblanco,[email protected] Abstract Several applications to represent classical or fuzzy data in databases have been developed in the last two decades. However, these representations present some limitations specially related with the system portability and complexity. Ontologies provides a mechanism to represent data in an implementation-independent and web-accessible way. To get advantage of this, in this paper, an ontology, that represents fuzzy relational database model, has been redefined to communicate users or applications with fuzzy data stored in fuzzy databases. The communication channel established between the ontology and any Relational Database Management System (RDBMS) isanalysedindepththroughoutthetexttojustifysomeoftheadvantagesofthesystem: expres- siveness, portability and platform heterogeneity. Moreover, some tools have been developed to define and manage fuzzy and classical data in relational databases using this ontology. Even an application that performs fuzzy queries using the same technology is included in this proposal together with some examples using real databases. Keywords: Ontologies, Fuzzy Relational Databases, Schemas, Prot´eg´e, Knowledge Representa- tion, Fuzzy Data. 1. Introduction clude most of the characteristics considered in other proposals, i.e, similarity relations5 or pos- Severalfuzzydatabasemodelsaredefinedinthe sibility distributions 33,35 to develop a complete literature 11,23 to represent fuzzy data in rela- fuzzy data representation model. But, in gen- tional databases (DB) but none of them have eral, fuzzy data representations present some been standardized and commonly accepted. problems: i) these representations are platform Some fuzzy data representations, such as the dependent, e.g., theproposalofMedinaetal. 29 proposal of Medina et al. 29, have tried to in- ∗Corresponding author. Published by Atlantis Press Copyright: the authors 1089 C. Martinez-Cruz, I. Blanco. and M.A. Vila works with Oracle(cid:13)c platform or Kacprzyk and portability and simplicity. Zadroznyproposal16 workswithMS.Access(cid:13)c , Moreover, the parallelism between the defi- ii) some proposals are incomplete, that is, most nition of tuples in the ontology and the defini- of them present partial views of uncertainty in tion of a database query has lead to the defini- DB representations, e.g. proposals that repre- tion simple fuzzy queries in the ontology. Con- sentfuzzinessintuplesandattributes35,inrela- sequently, an analysis of how a fuzzy query is tionships43 orvaluesexclusively5,iii)proposals defined and performed in a fuzzy database is that only make fuzzy queries, e.g. Bosch et al. described in this proposal as well. Also, simi- 4 or iv) proposals that are not compatible with larly to previous developments, a new Prot´eg´e currentSemanticWebtechnologiesbecausethey plug-in that helps the user to generate fuzzy do not use ontology web languages to be repre- queries as ontologies and execute them on fuzzy sented, only Martinez-Cruz et al. proposal 25 databaseshasbeendevelopedandincludedhere. establishes a first approach that develops such a In this comparison, the advantages of defining characteristic. fuzzy queries using the ontology are highlighted Thus, a solution to these problems was pre- becauseofthedecreaseofcomplexityinthedef- sented in Martinez-Cruz et al. proposal25 where inition process and the increase of system inde- an ontology describes a fuzzy database repre- pendence. Also, aweb-understandabledatabase sentation model. This ontology acts like an representationisavailableoncetheontologyhas external layer where fuzzy or non-fuzzy data beendefinedinOWL(ontologyweblanguage)1. can be represented regardless of any database Thus, fuzzy database schemas and fuzzy queries model restriction, in a flexible way. In this pro- can be indexed within the Semantic Web when posal, aprototypewasdevelopedtodefinefuzzy necessary. database schemas easily. But, the ontology does not represent fuzzy domains and constraints, Finally, this proposal is tested on real fuzzy which are an important part of the fuzzy re- databases and consequently, some applications lational model. Also, the development lacks of have been developed to make fuzzy schemas themanagementoffuzzydataorafurtherstudy and data definition process easier for the user. abouttoolsthatareavailabletobeusedinstead. They are developed using the ontology manage- ment tool, Prot´eg´e and allow transactions to In this paper the authors solve the pre- be executed with different and heterogeneous vious work shortcomings and include new re- databases platforms at the same time. search about the establishment of communica- tion between the ontology and the fuzzy rela- A brief review of fuzzy databases and on- tional database management system (RDBMS) tologies is presented in section 2, which is fol- as an extension of the paper presented in 24. lowed by a description of the fundamentals of Three different database implementations have the proposed ontology. The extension and fi- beenidentifiedtoestablishsuchcommunication: nal description of the ontology that defines the RDBMSs that include fuzzy functionality inter- fuzzy relational database model is presented in nally, RDBMSs which include procedural fea- section 3. The architecture of the system and tures and RDBMSs which cannot execute any the data flow between the ontology and hetero- SQL procedures. Furthermore, several devel- geneousDBtechnologiesarepresentedinsection opments to manage fuzzy data through the on- 4. Also, adescriptionofthedevelopedtoolsand tology have been developed and compared with their functionality are shown in section 5. A alternative mechanisms to perform similar op- performance analysis of these tools and a com- erations. This comparison justifies the advan- parison with others are presented in this section tages of using ontologies instead of accessing aswell. Finally,conclusionsarediscussedinsec- fuzzy databases directly, such as expressiveness, tion 6. Published by Atlantis Press Copyright: the authors 1090 An Ontology for representing Fuzzy RDB 2. Fundamentals tension of Data Definition Language (FDDL) and Data Management Language (FDML). Theproposalpresentedhereisbasedontwodif- ferent representation models: fuzzy relational 2.2. Ontologies and Databases databases and ontologies. Both models have been merged in an ontology that represents the Formal ontology definitions, classifications, fuzzy relational database model. A brief review methodologies, tools, languages and operations ofthesemodelsandafirstapproximationtothis are described extensively in literature (see com- ontology are described in this section. pilations 13,38,41). In general, an ontology is a knowledge representation model whose popular- ity has increased due to its capability of repre- 2.1. Fuzzy Databases senting semantics in the Web. Nowadays, they Several relational database model extensions to have nothing in common with their initial defi- define fuzzy data have been proposed during nition that represents only a formal and agreed the last four decades. Since the first relational knowledge of a specific domain in a collabora- database proposal was defined by Codd 8 and tive way. Some of the main characteristics of the fuzzy set theory was defined by Zadeh’s 45, ontologies are 28: a frame that extends the relational database model to manage fuzzy data was opened. Com- • Ontologies represent semantics of a domain in a formal way. pilations like Ma’s 23 and Galindo’s 11 present a complete overview of these extensions: • TheWebconsortiumW3C hasacceptedOWL and RDF as standard languages to represent • Some proposals represent the uncertainty in ontologies. table tuples and attributes35. • Data are not required to be defined in ontolo- • Some proposals represent fuzziness in the re- gies but schemas are. lationshipamongdatawherenon-fuzzyvalues • Theoretically, ontologies model a general are presented but operators are fuzzy 5. knowledgeofadomain,buttheyarenotwork- • Other proposals allow the questioning of rela- ing in practice. There are several approaches tional databases using fuzzy queries 4. of generic ontologies that model the whole re- • Some proposals allow uncertainty to be de- ality like Cyc 21 or KR ontology 40. However, fined in data. Fuzzy data can be modelled currentontologiesrepresenttheknowledgere- with, e.g., possibility distributions33, similar- quired to solve specific problems as databases ity relations 39, etc. do. • Ontologies require reasoning tools to ensure Finally, some fuzzy relational data mod- their data integrity. els have tried to include most characteristics • The number of ontologies is increasing expo- previously described, such as Rudensteiner et nentiallyduetotheiruseintheSemanticWeb al. 36 or Medina et al.29 proposals. The lat- and their popularity. ter, which is called GEFRED, represents fuzzy data using possibility distributions and similar- Thus, relational database representation ity relations. This model extends the relational model has certain similarities with ontologies database model with fuzzy data using the ele- since ontology classes, attributes and axioms mentsdefinedintable1. Anarchitectureforthis can be interpreted as tables, attributes or con- theoretical model has been defined in FIRST29, straints respectively. However, these correspon- whereafuzzydatabasecatalogisdesigned. Fur- dences are not so trivial. Some authors con- thermore,anextensionofSQLcalledFuzzySQL siderdatabaseschemasaslight weight ontologies (FSQL) manages fuzzy data 3 through the ex- because they lack a semantic description given Published by Atlantis Press Copyright: the authors 1091 C. Martinez-Cruz, I. Blanco. and M.A. Vila Table 1. Fuzzy Basic data types defined in 29 Fuzzy DT Name and Example Description FType1 Any numeric value It is only used in fuzzy queries. FType2 Crisp (5) A numeric value, e.g. 5. FType2 Approx (5) Approximateto5. Itisrepresentedbyatrianglemembershipfunc- tion where 5 has the highest membership value. FType2 Interval[4,6] It is represented by an interval membership function where the gap between 4 and 6 has the highest membership value. FType2 Trapezoid[4,5,6,7] This trapezoidal membership function returns the higher value for input values between 5 and 6. FType2/- Unknown Attribute values that are not known. FType3 FType2/- Undefined Attribute values that are not applicable. FType3 FType2/- Null Attribute values that have not value. FType3 FType2 Label (Tall) This linguistic label is associated with any of the previous struc- tures, e.g., Tall could be associated with Approx(1.75) value. FType3 Discrete Value (Blond A label related to other labels by a similarity relationship, e.g., Hair) Blond Hair is similar to Red Head Hair with a degree of 0.7. FType3 Discrete Distribution ItrepresentsasetofDiscreteValuesandtheircertaintydegree. E.g. Blond Hair, 0.5 and Brown Hair, 0.7 by the logical rules represented in ontologies 13. a database definition to ensure system effi- Moreover, databases present further differences ciency. There are two alternatives to develop from ontologies: this task but the most usual one uses On- tologies Based Databases (OBDB) 14 to store • Data management is more efficient than on- an ontology using a common and unique data tologies. model. Jena 34, Sesame18 and other develop- • Data consistency is ensured due to the nor- ments 44 have implemented it. The second al- malization process. ternative defines databases using information • Any kind of data can be represented in an al- extracted from an ontology; classes, relations ready developed DBMS: objects, temporal in- and constraints. An example of this kind of formation, multimedia objects, logical rules, application is OntoDB. spatial data, etc. • Generate ontologies from databases. It is • There is a standardized language, SQL. the most common approach due to the large amount of existing databases. There are sev- Currently, bothtechnologiescoexisttogether eral proposals which use conceptual 14,22, log- to ensure the best efficiency. Several approaches ical schemas 15 or data (tuples)42 and even have been defined to communicate ontologies database queries19 to generate the ontology. with databases. These approaches can be sum- These proposals generate the domain ontol- marized below: ogyfromthedatasourceautomatically. Other proposals implement the relational model as • Generate databases from ontologies. This an ontology and database schemas as ontol- approach starts from an ontology with a ogy instances, some examples of this imple- large amount of information that requires Published by Atlantis Press Copyright: the authors 1092 An Ontology for representing Fuzzy RDB mentation are in Champing et al.7, Laborda 3. A Complete Description of the Fuzzy et al.31, Calero et al.6 and Martinez-Cruz et Relational Database Ontology al.25 proposals. • Map databases and ontologies. This approach The Fuzzy Catalog Ontology 25, that is sum- is used when a database and the ontology is marized above, defines most of the complete already developed. Then, only the establish- SQL description and fuzzy structures defined ment of the mappings are required. Datage- in the GEFRED model and FIRST architec- nieapplication12 developedbyGennarietal., ture. However, two new classes are included R2O and Web-PDDL languages developed by in the ontology to complete the definition of Barrasaetal.2andDouandLePendu9respec- fuzzy data in it. These classes, previously in- tively are some examples of this approach. troduced in 24, are defined in detail below: 2.3. Fuzzy Schema and Data Ontology An ontology to represent a fuzzy relational databasewasfirstlypresentedbyMartinez-Cruz et al.25. The defined ontology is called Schema Ontology or Fuzzy Catalog Ontology from now on because it includes all the components of the SQL standard (only relational model) 10 ex- tended with some of the GEFRED29 structures to represent fuzzy relational database schemas (see section 2.1). The main classes to represent fuzziness in database schemas are: Fuzzy Table, Fuzzy Column, Fuzzy Data Type. They are di- vided in three: FDataType1, FDataType2 and FDataType3, according to those described in ta- ble 1, Fuzzy Structures or Fuzzy Values. They aredescribedintable1,FuzzyLabels,FuzzyDis- cretes. Fig. 1. Fuzzy Catalog Ontology Domain. structures. In this proposal, database definition pro- cess has two stages, the first one defines a fuzzy schema by instantiating the Fuzzy Cata- • Fuzzy Domain: it defines any fuzzy column log Ontology and the second one generates the domain. In contrast to ordinary database database schema as a common Domain Ontol- columns, a fuzzy column requires a domain to ogy (also called Data Ontology25). The purpose be defined instead of a data type. Fuzzy do- ofthisDomainOntology definitionisthestorage mains are defined not only by data types but ofdatabasetuplesasontologyinstancesbecause also by labels or discrete values and any at- it represents a fuzzy schema as a set of classes, tribute constraint, as well. Moreover, a fuzzy attributes and constraints. This ontology is au- domain can define several attributes. The re- tomatically generated and the generation pro- lationshipbetweenthefuzzydomainclassand cess is addressed in 25. other classes of the ontology are shown in fig- Finally, this proposal is a first prototype of ure 1 (see 25 for further details of the ontol- an ontology that is finished with the inclusion ogy). of fuzzy domains and fuzzy constraints. In the • Fuzzy Constraints: represent those con- next section this ontology is described using a straints defined in fuzzy domains. For exam- real database example. ple, Label Const constraint means that no la- Published by Atlantis Press Copyright: the authors 1093 C. Martinez-Cruz, I. Blanco. and M.A. Vila bel are allowed in a domain. A description fuzzy structure according to the fuzzy data of fuzzy constraints defined in the ontology is type. For example, if the attribute Tavg: Av- showninfigure2whereSQLandfuzzyclasses erage of temperature is a FType2, the range areinwhiteandgreybackgroundrespectively. goes to the super-class FType2 Structure that represents: Label, Trapezoidal, Interval, Ap- The Fuzzy Catalog Ontology described in OWL proximate, Crisp, Null, Unknown and Unde- is available for downloading in the URL: fined classes. http://wwwdi.ujaen.es/cmcruz/research/ • Ifdomainincludesfuzzyconstraints,therange ontologies/fdtscho.owl of the object property goes to the specific fuzzy structures that are not constrained. For example, if the fuzzy domain established for the Tavg: Average of temperature attribute is a FType2 but Unknown or Undefined val- ues are not allowed, the range of this property goes to: Label, Trapezoidal, Interval, Approx- imate, Crisp and Null structures, instead of going to the super-class FType2 Struct. Fig. 3. Ontologies involved in the definition process. Fig. 2. Fuzzy Catalog Ontology Constraints. struc- The resulting ontology structure is a mixed tures. ontology (see figure 3) containing the Fuzzy The definition process of a database schema Catalog Ontology, instances defining a database that contains fuzzy data consists of instantiat- schema and the Domain Ontology. The last on- ing the proper classes and attributes included in tology is only required if data are defined in the the ontology. After this definition, two different ontology. operations can be performed: i) the translation An example of a land characteristics of this schema to a RDBMS, ii) the definition database is used throughout this proposal and of database data (tuples) in the ontology. The the complete database description is available last one requires to generate the equivalent Do- in 27. In this example, instantiation of several main Ontology. A new guideline to develop this Fuzzy Catalog Ontology classes to define this Domain Ontology 25 is included to manage the database schema is required. A small selection new classes: Each fuzzy column is defined as a of these instances is shown in table 2 and figure functional object property. The range of this 4. They represent fuzzy and classical attributes: property depends on the fuzzy domain: latitude (Lat), average of temperature (Tavg) and physiography, fuzzy domains: Dom physiog • If domain is defined only by fuzzy data types, and Dom Tavg, fuzzy constraints: FC1 Tavg, the range of the object property goes to the FC2 Tavg, labels and discrete labels (Low, Flat, Published by Atlantis Press Copyright: the authors 1094 An Ontology for representing Fuzzy RDB Slope, etc.), trapezoidalrepresentationsandpri- FType2 Structure sub-class but not Unknown, marykeys. Remaininginstancesfollowthesame Undefined sub-classes. A complete set of in- pattern, no matter whether fuzzy data or not. stances of this schema is available in OWL from the following URL : ID Instance of Value or http://wwwdi.ujaen.es/cmcruz/research/ Range ontologies/landonto.owl Location Table Ref: Lat, phys- iography, Tavg, ... Lat Base Column Ref: DT lat DT lat Numeric Values:2,8 PK Loc Primary Key Ref: Lat, Long physiographyFuzzy Column Ref: Dom physiog Tavg Fuzzy Column Ref:Dom Tavg Dom physiogFuzzy Domain Ref: TD physiog, .. Dom Tavg Fuzzy Domain Ref: TD Tavg, FC1 Tavg, FC2 Tavg,.. Fig. 4. Partial example of land characteristics TD physiog FType2 Struct Value: 1 database schema. TD Tavg FType3 Struct Values: 3,4 Ref: Finally, the domain ontology provides a new Float Flat Discrete Definition - tool to define simple fuzzy queries. This utility Slope Discrete Definition - consists of defining the query condition clauses Flat-Slope Discrete Relation Value: 0.5 Ref: inthedomain ontology propertyvalues. Thus,a Flat and Slope query can be represented as an ontology, trans- Low Label Definition Ref: latedintoSQLorFuzzySQLandlater,queryre- Low Tavg TD sultscanbereturnedinthesameontologystruc- Low Tavg TDTrapezoid Value Values: ture. This representation tries to take advan- [0,0,6.5,8.5] tage of the ontology language flexibility where FC1 Tavg Nullability ConstraintValue: true data property values are not limited to specific FC2 Tavg Unknown Constraint Value: true data types and ontology comments allow stor- ... ... ... age of any value. Therefore, this proposal does Table 2. Land ontology schema instances. not add new elements to the proposed ontology Duetospacelimitations,thecompleteexam- structure, it tries to minimize the sytem com- ple is available in OWL in the URL: plexity. http://wwwdi.ujaen.es/cmcruz/research/ ontologies/land.owl Thus, a query is represented as set of in- The previous definition of the land charac- stances of each table involved in the query in teristics schema is translated into a land do- the domain ontology. Each instance represents main ontology following the rules described in one query condition or the visibility statement 25,24 and above. A partial view of the re- of the query attributes. Then, if the attribute is sulting domain ontology is displayed in table addressed to a data type property in the ontol- 3 and figure 5. In this example, the range ogy, the condition clause is set in a string whose of physiography property is a Ftype3 Structure value involves writing the condition completely, class and the range of Tavg property is any includingtheoperatorandthevalueorattribute Published by Atlantis Press Copyright: the authors 1095 C. Martinez-Cruz, I. Blanco. and M.A. Vila Fig. 5. Partial example of land characteristics database domain ontology. to which it is compared. On the other hand, the ble where the average of temperature (tavg) is attribute visibility is set in a data type property equal to “medium” in a degree of 0.8 and the storing the ”visibility” string constant. If the physiography is not equal to “bottom slope” in a attribute is addressed to an object property in degree of 0.9. The syntax of the query in FSQL the ontology, the condition clause is set in the is written below: rdf:comment of the instance that represents the SELECT Lat, Lon FROM Location value. If the condition does not involve a value WHERE butitinvolvesotherattribute,theinstancetobe Tavg FEQ $medium THOLD 0.8 and included is the one corresponding to the nulla- Physiography NEQ ’$Bottom Slope’ bility struct. The same operation is made to set THOLD 0.9 the visibility statement in the object properties. Table 4. Instances of a query definition in the domain About the logical condition joiners AND and ontology of the land characteristics schema. OR, this proposal establishes the definition of the conditions in a clausal mode, that is, avoid- ID InstanceProperty Value ing the use of brackets. of or Range Table 3. Partial domain ontology of the Land database I1 Location Tavg I2 example. I2 Label rdf:comment:“FEQ $mediumTHOLD0.8” Class Property Range or value I2 Label LabelId Medium Location Lat http://www.w3.org instance /2001/XMLSchema#float I1 Location Physiography I3 Location Tavg Trapezoid, Crisp, Approx, I3 Simple rdf:comment: “FEQ Interval, Null, Label $Bottom Slope Location Orientation Ftype3 Struct THOLD 0.9” Location Pavg Ftype2 Struct I3 Simple DiscreteID Bottom Location Slope Ftype2 Struct Slope Analytic Sand Ftype2 Struct instance ... ... ... I1 Location Lat “Visible” I1 Location Long ’“Visible” Following the previous example, a query is represented in the domain ontology that is de- Thedomainontology isinstantiatedtorepre- scribed in figure 5 and table 3. This query gets sentthisquery,andtheseinstancesareshownin the latitude and longitude from the location ta- table 4. The where clauses are included in the Published by Atlantis Press Copyright: the authors 1096 An Ontology for representing Fuzzy RDB ontology as rdf:comments because the proper- tology. Summarizing, there are three possible tiestavg and physiography areobjectproperties. communication scenarios with RDBMS that are Thus, they are included in the instances of the shown in figure 6 and described below. A deep Label and Simple classes respectively and they study of these scenarios can be found in 26: have associated the label definition instances: Medium and Bottom Slope which are obtained Scenario 1. DB Systems with FSQL capabili- from their fuzzy domains. The visibility of this ties. These systems do not require trans- query is set as data type properties, and con- lationintoSQLbecauseprocedurestoexe- sequently, no new instances are required to be cute FSQL commands are included. They defined, only the establishment of the ’visible’ are the most efficient fuzzy RDBMS im- constant in the attribute value. Notice that it is plementations because the entire process notnecessarytoinstantiatelocation tableagain, is done in the same platform. Not all the because the query does not involve any OR con- RDBMSs include programming capabili- dition nor is one attribute involved in the visi- ties. bility and where clause at the same time. Scenario 2. DB Systems with programming ca- pabilities but not FSQL. Fuzzy queries can 4. Architecture Description be performed within the system by mean of functions and procedures included in SQL sentences but translation from FSQL toSQLhastobedoneexternally. Thisop- tion improves the statement execution be- OngOtioenlsot(cid:13)ioe-(cid:13)lso(cid:13)g(cid:13) cause it can be partially executed within Application(cid:13) the system, so the response time is re- duced. Scenario 3. DB Systems with no program- FSQL(cid:13) ming capabilities. When the system is Adaptator(cid:13) only capable of representing and storing data, fuzzy data management must be Functional(cid:13) SQL Adaptator(cid:13) done outside the database completely. An Module(cid:13) with functions(cid:13) external module is in charge of coordinat- ing the process of executing SQL state- ments. This is the least efficient system SQL(cid:13)Ext(cid:13).(cid:13) SQL(cid:13)Ext(cid:13).(cid:13) SQL(cid:13)Ext(cid:13).(cid:13) because the entire process is implemented DBMSs(cid:13) DBMSs(cid:13)Func(cid:13).(cid:13)Ext.(cid:13) DBMSs(cid:13) FSQL(cid:13)Ext.(cid:13) outside the RDBMS and consequently the response time is the highest. RDBMS without(cid:13) RDBMS with(cid:13) RDBMS with(cid:13) functional(cid:13) functional(cid:13) FSQL capabilities(cid:13) Summarizing, all these scenarios imply a capabilities(cid:13) capabilities(cid:13) SQL translation, the sentence execution and Fig. 6. Database communication scenarios. the results presentation (if applicable). But these operations are performed in different plat- In this proposal, heterogeneous relational forms according to the system capabilities and database management systems (RDBMS) are included libraries. involvedindatadefinitionandmanagementpro- Then, each possible operation that can be cesses. These RDBMSs require different im- performed in a database (schema definition and plementations to build a unified mechanism to datamanagement)isanalysedineachofthepre- manage fuzzy information provided by the on- viously defined scenarios. Published by Atlantis Press Copyright: the authors 1097 C. Martinez-Cruz, I. Blanco. and M.A. Vila 4.1. Schema and Data Definition Later,aschema definition canbedoneinthe Process RDBMS. This schema is defined in the Fuzzy Catalog Ontology using an ontology manager such as the one developed in section 5 of this proposal. Thethreeoperations,thattheschema definition process involves, are shown in figure 7 and described below: 1. Instantiation of the Catalog Ontology is represented by arrow (b) in figure 7. The schema is fully described by the instantia- tion of the Fuzzy Catalog Ontology. Thus, the definition of the schema lacks any DB implementation restriction. 2. Domain ontology conversion is repre- sented by arrow (c) in figure 7. The pre- vious schema definition, that is available as instances of the Fuzzy Catalog Ontol- ogy, can be translated into a real ontology, Fig. 7. Data flow description. called Domain Ontology in figure 7. This ontology corresponds to the schema of a Data flow between users and a final storage database but internal schema definitions system is a complex procedure because of het- are omitted (section 2.3). Translation erogeneous formats involved in the schema defi- rules have been implemented as a Prot´eg´e nition process. The data flow for the definition plug-in application (section 3). The re- of fuzzy schemas and data, is shown in figure 7 sulting OWL Ontology also contains some and is described below. classes and instances imported from the At first, before any schema definition is per- Fuzzy Catalog Ontology. formed,theRDBMScatalogshouldbeextended with new structures to store fuzzy data (see sec- 3. RDBMS Communication Scenarios. The tion 2.1 for further details). This process should database communication, which is called be done once for each RDBMS implementation DBC2andrepresentedbyarrow(d)infig- and such installation depends on the RDBMS ure 7, works as follows depending on the system features and library capabilities. Conse- scenario†: quently, if a database has no functional capabil- ities, only the fuzzy catalog structures would be • Scenario (1) sends FSQL sentences to installed and any management operation should the RDBMS. These sentences are equiv- bedoneoutsidetheRDBMS,asdescribedprevi- alent to fuzzy DDL. An example of a ously. TheDBC1 relation, whichisdescribedin create table sentence that includes fuzzy figure 7 arrow (a), shows this catalog extension attributesisshownbelow. Thisexample process within a RDBMS. This stage applies to is part of the database land characteris- scenarios (1), (2) or (3). Thus, the same catalog tics followed throughout this paper and structures are stored in any RDBMS regardless further detailed in 27: of object identification issues and different data CREATE TABLE Location ( types. lat NUMERIC NOT NULL, †A complete description of the meaning of the FSQL language can be found in 3,11 Published by Atlantis Press Copyright: the authors 1098