Standard XML format does not allow for imprecise or incomplete values. This is one of the requests imposed on this format by many real-word usages. Using fuzzy logic in order to introduce indefiniteness in XML has been researched in several different papers in the last decade. While these papers were mostly focused on setting up theories and the syntax, this paper has practical usage as its main goal. Application called 'Fuzzy XML editor' was created and described in this research. This editor is intended to work with fuzzy XML and to support XSD and DTD schemas.
Theory
XML (Extensible Markup Language) has revolutionized fields of data storage and transfer in the last decade. There are many positive sides to XML which made it de facto a standard for many different uses. Values stored in XML elements and attributes are absolutely in accordance with their definition. Also, the whole structure of XML file is predefined and non-changeable. However, in reality, most information comes in the form of imprecise or incomplete values (e.g. fast car, tall building). Storing imprecise information is not one of the things standard XML supports. Fuzzy sets and fuzzy logic are theories used in many different fields where the use and processing of imprecise and incomplete information were needed. Adding fuzzy logic on ∗Corresponding author, tel. +381 64 289 8959 top of standard XML would result in XML containing insufficiently defined and imprecise information.
Several papers dated to previous decade can be found, discussing the use of fuzzy logic in defining XML indefiniteness. However, the published papers focus mostly on setting up theories and defining syntax. There are only a small number of papers that deal with the implementation process and practical usage. Some simplistic implementations were presented, limited to a restricted set of instructions which often do not meet the needed functionality for any sort of practical use. Without practical usage, it is hard to get a clear view of actual possibilities of different theories. Also, the performance and complexity of implementing seemingly good syntax solutions do not always have to be satisfactory. In order to overcome these problems, this paper focuses on practical solutions in real-world environment. This is achieved by implementing to a level of usable applications. For numerical computation, MATLAB (Matrix laboratory) software was used (for the sake of simplicity and good performance). MSSQL (Microsoft SQL Server) is used as underlying database with XQuery queries. Fuzzy priorities and thresholds will be used and implemented in XQuery queries for the first time. However, prioritized fuzzy XQuery is out of scope and will be left for a subsequent paper.
Second chapter provides an overview of existing papers, in the field of fuzzy logic usage with XML. Chapter 3 explains XML indefiniteness, presenting extended XSD (XML Schema Definition) and DTD (Document Type Definition) schemas for indefinite XML. The features of application specifically developed for this paper are presented in details in Chapter 4. 2.
Related research presented in this paper was conducted
in the last five years at the University of Novi Sad. The
main topic was implementation of system capable of using
priority fuzzy logic with relational databases. In addition,
complete fuzzy relational database application solution was
designed and implemented [
The use of fuzzy logic in indefinite XML is an area where multiple papers have been presented in the last decade. Most influential research topics are: defining indefiniteness in XML values and defining indefiniteness in XML structure.
For defining indefiniteness in XML structure usually XPath
and XQuery languages were extended by the authors.
Presented solutions find elements in XML documents whose
positions are not exactly stated. Examples of such solutions
are given in: [
Most significant form of XML indefiniteness is the
indefiniteness in XML values. For structural definitions of fuzzy
XML documents, XML schemas are usually used. However,
in some works schema graphs were used for the same
purpose. Such examples are presented in: [
XML documents are often stored into databases that
support XML. Papers related to this subject discuss extending
database models by introducing fuzzy types or extending the
SQL and XQuery syntax by using fuzzy elements. See more
on this topic in following papers: [
In this paper implementation of indefiniteness in XML values is researched. This assume definition of XML model that allows storing of fuzzy values. The main focus is on the implementation of practical fuzzy XML applications.
Best solutions presented in related works were combined
and new model for XML fuzzy data storage was developed.
For instance, [
Membership function is most important when it comes to fuzzy set usage. It is not an easy task to define membership function, while its storage and processing leverage the level of complexity of the implementation. There are two ways of building such solution. The first is that fuzzy set should include certain number of simple and well-known function types (e.g. increasing, decreasing, triangular, trapezoidal). In choosing groups of fuzzy sets to implement, one needs to pay special attention to the choice of sets. The purpose is to cover as many real systems as possible. Still, regardless of how many fuzzy sets are introduced, they are still restricted. So, cases whose functions are not described are still unreachable to such solutions.
The second option is to define syntax which can model the fuzzy set. In this paper, this option was selected due to its versatility. XML is metalanguage, intended to offer expandability, so there was no need to specifically change XML language syntax to support fuzzy logic. Still, in order to design XML structure flexible enough to enable defining wide variety of fuzzy sets, there are certain conditions. These are presented below.
For example, there is an XML element, <temperature>,
which is undefined and is of a fuzzy type. The element can
contain an arbitrary number of <fuzzy> elements which
represent fuzzy sets. All fuzzy sets are uniquely named using
the name attribute, such as <fuzzy name=”cold”>. Fuzzy
sets are further defined by <function> - membership
functions which can vary in number. Membership functions
can be constrained by supplying minValue and maxValue
attributes. As presented here: <function minValue=”0”
maxValue=”10”>; this cannot overlap within a single fuzzy
set. The default values of these attributes are maxValue:
plus infinity, minValue: minus infinity. The value of the
<function> element defines the membership function for
certain area defined by the minValue and maxValue
attributes. In this value x is a variable that collects values
from given intervals. The level of membership is taken from
the interval [
The easiest way to define the previously described fuzzy type is to use some of the existing XML schemas. XSD schema which defines the described fuzzy type is presented below. The element containing function describes part of the membership function limited by minValue and maxValue constraints. The functions element classifies function parts into a complex membership function. The fuzzy element is a fuzzy set which is defined by a set of membership functions. Fuzzy XSD schema is presented in listing 1
Listing 1: XSD schema for fuzzy element 1 <x s: sc h e m a i d=”Fuzzy ” elementFormDefault=” q u a l i f i e d ” x m l n s: x s=” h t t p : //www. w3 . or g /2001/ XMLSchema”> 2 <xs:complexType name =” f u z z y ”> 3 <x s : s e q u e n c e> 4 <x s : e l e m e n t name =” f u z z y ” minOccurs =”1 ” maxOccurs =”unbounded” type=” f u n c t i o n s ” /> </ x s : s e q u e n c e> </ xs:complexType> <xs:complexType name =” f u n c t i o n s ”> <x s : s e q u e n c e> <x s : e l e m e n t r e f=” f u n c t i o n ” minOccurs =”1 ”
maxOccurs=”unbounded ”/> </ x s : s e q u e n c e> <x s : a t t r i b u t e name=”name ” type=” x s : s t r i n g ”/> </ xs:complexType> <x s : e l e m e n t name=” f u n c t i o n ”> <xs:complexType> <x s : s i m p l e C o n t e n t> <x s : e x t e n s i o n b ase=” x s : s t r i n g ”> <x s : a t t r i b u t e name=”minValue” type=”
x s : s t r i n g ” /> 20 <x s : a t t r i b u t e name=”maxValue ” type=” x s : s t r i n g ” /> 21 </ x s : e x t e n s i o n> 22 </ x s : s i m p l e C o n t e n t> 23 </ xs:complexType> 24 </ x s : e l e m e n t> 25 </ x s: sc h e m a>
So, by referencing Fuzzy.xsd schema in a XML document and using Fuzzy type for element type, indefinite fuzzy XML can be written. An example of this is given in listing 2.
Listing 2: Using Fuzzy XSD schema 1 <?xml v e r s i o n=” 1 . 0 ” e n c od i n g=”u t f −8”?> 2 <x s: sc h e m a i d=”Test ” elementFormDefault=” q u a l i f i e d ” x m l n s: x s=” h t t p : //www. w3 . or g /2001/XMLSchema”> 3 <x s : i n c l u d e schemaLocation =”Fuzzy . xsd ”/> 4 <x s : e l e m e n t name=”measurement”> 5 <xs:complexType> 6 <x s : s e q u e n c e> 7 <x s : e l e m e n t name=”name ” type=” x s : s t r i n g ”/> 8 <x s : e l e m e n t name=” l o c a t i o n ” type=” x s : i n t ”/ > 9 <x s : e l e m e n t name=”time ” type=”x s: d at e Ti m e ” /> 10 <x s : e l e m e n t name=”t e m p e r at u r e ” type=” f u z z y ”/> 11 </ x s : s e q u e n c e> 12 </ xs:complexType> 13 </ x s : e l e m e n t> 14 </ x s: sc h e m a>
Same can be achieved by using other types of XML schema documents. Using DTD schema for the same task is presented in listing 3.
Listing 3: DTD schema for fuzzy element 1 <? xml v e r s i o n=” 1 . 0 ” e n c od i n g=”UTF−8”?> 2 <!ELEMENT measurement ( t e m p e r at u r e )> 3 <!ELEMENT t e m p e r at u r e ( f u z z y+)> 4 <!ELEMENT f u z z y ( f u n c t i o n+)> 5 <! ATTLIST f u z z y name CDATA #REQUIRED> 6 <!ELEMENT f u n c t i o n (#PCDATA)> 7 <! ATTLIST f u n c t i o n 8 minValue CDATA #REQUIRED 9 maxValue CDATA #REQUIRED>
Full example of fuzzy XML documents defined in accordance to presented syntax, storing air temperature measurements are given in listing 4.
Listing 4: Fuzzy XML example 1 <measurement> 2 <name>New s t a t i o n</name> 3 <l o c a t i o n>41</ l o c a t i o n> 4 <time>2012−02−03 10 : 3 0</ time> 5 <t e m p e r at u r e> 6 <f u z z y name=” c o l d ”> 7 <f u n c t i o n maxValue=”0 ”>1</ f u n c t i o n> 8 <f u n c t i o n minValue=”0 ” maxValue=”10 ”>−1/(Max −Min ) ∗x + Max/(Max−Min )</ f u n c t i o n> 9 </ f u z z y> 10 <f u z z y name=”hot ”> 11 <f u n c t i o n minValue=”10 ” maxValue=”20 ”>1/(Max −Min ) ∗x − Min /(Max−Min )</ f u n c t i o n> 12 <f u n c t i o n minValue=”20 ”>1</ f u n c t i o n> 13 </ f u z z y> 14 </ t e m p e r at u r e> 15 </ measurement>
The value of fuzzy elements can include real text, the so called linguistic definitions. They start with a # sign. These variables are predefined fuzzy sets. Example of such definition can be found in listing 5.
Listing 5: Linguistic definition example 1 <f u z z y name=” c o l d ”>#Maybe</ f u z z y>
Application ’Fuzzy XML editor’ is implemented to demonstrate practical aspect of working with fuzzy XML syntax. This application enables creation and working with fuzzy XML, XSD and DTD documents, and has been developed specifically for the needs of this paper. Main application window is presented on figure 1.
.NET framework and WPF technology were used in implementation of this application. Fuzzy XML tool components and their mutual relations are presented in figure 2.
The application consists of several logical modules organized according to the MVVM (Model View View-Model) pattern and its principles.
The Data layer is the lowest level, dealing with the data storage. The storage options are: text files (file system component) and database (database component). Microsoft SQL server 2008 R2 support was implemented in order to work with the database. Its potential for working with XML is extended by fuzzy elements.
The Model layer contains several components, where each has a task to communicate with certain object types. The XML model supports working with fuzzy XML objects, while the DTD and XSD models are in charge of working with fuzzy XML schemas. The XQuery model implements working with fuzzy XQuery, and includes the support for priorities and thresholds. However, fuzzy XQuery is out of scope of this paper. Each of the components can implement the part for working with the fuzzy syntax apart from working with the standard language syntax.
The View-Model layer makes it possible to communicate with the layer below and consists of several modules. The Command group classifies modules for working with commands that implement interfaces for model approach. The Syntax Validation component enables validation of document syntax. The Fuzzy group enables working with membership functions and fuzzy linguistic variables. The Fuzzy group relies on the Matlab module which is an interface to external application - MATLAB. Calculations of the membership level are done using MATLAB libraries.
The View layer is the last layer. It implements the user interface, so that the user can perform functionalities defined in the Command group. The Main Window component is the main application window which includes the user controls from the Controls group and enables calling of the other independent dialogue windows from the Dialogs group.
Executable version and other data of the application can be found at http://www.is.pmf.uns.ac.rs/fuzzydb. 5.
This paper successfully unites the process of defining syntax and implementing it. An application solution that enables usage of the fuzzy logic constructs with XML data has been provided. Users are given a possibility to define the arbitrary membership functions, and their computation is achieved in real time with the usage of the MATLAB software. The practical side of this implementation and its satisfactory performance has been demonstrated.
The presented application solution will be a basis for further development of XML indefiniteness. In future work, definition and implementation of the fuzzy XQuery interpreter that allows the usage of priorities is planned. Also, the emphasis of future work is on improving the implemented functionalities and the syntax, further improvement of the performance and finally, introduction of indefiniteness in the XML structure.
Research was partially supported by the Ministry of Science and Technological Development of Republic of Serbia, through project no. OI-174023 ’Intelligent techniques and their integration into wide-spectrum decision support’. [23] Z.M. Ma. Fuzzy database modeling with XML.
Springer, New York, February 2005. [24] Z.M. Ma, L. Yan, and F. Zhang. Modeling fuzzy information in UML class diagrams and object-oriented database models. Fuzzy Set. Syst. 186(1):26–46, January 2012. [25] M. Koyuncu. Intelligent fuzzy queries for multimedia databases. Int. J. Intell. Syst. 26(10):930–951, Jul 2011.