<?xml version="1.0" encoding="ISO-8859-1"?><article xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance">
<front>
<journal-meta>
<journal-id>1405-5546</journal-id>
<journal-title><![CDATA[Computación y Sistemas]]></journal-title>
<abbrev-journal-title><![CDATA[Comp. y Sist.]]></abbrev-journal-title>
<issn>1405-5546</issn>
<publisher>
<publisher-name><![CDATA[Instituto Politécnico Nacional, Centro de Investigación en Computación]]></publisher-name>
</publisher>
</journal-meta>
<article-meta>
<article-id>S1405-55462006000200007</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[A Unified Methodology to Evaluate Supervised and Non-Supervised Classification Algorithms]]></article-title>
<article-title xml:lang="es"><![CDATA[Una Metodología Unificada para la Evaluación de Algoritmos de Clasificación tanto Supervisados como No-Supervisados]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Godoy Calderón]]></surname>
<given-names><![CDATA[Salvador]]></given-names>
</name>
<xref ref-type="aff" rid="A01"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Martínez Trinidad]]></surname>
<given-names><![CDATA[José Francisco]]></given-names>
</name>
<xref ref-type="aff" rid="A02"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Lazo-Cortes]]></surname>
<given-names><![CDATA[Manuel S]]></given-names>
</name>
<xref ref-type="aff" rid="A03"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Díaz de León Santiago]]></surname>
<given-names><![CDATA[Juan Luis]]></given-names>
</name>
<xref ref-type="aff" rid="A04"/>
</contrib>
</contrib-group>
<aff id="A01">
<institution><![CDATA[,IPN Centro de Investigación en Computación ]]></institution>
<addr-line><![CDATA[México D. F.]]></addr-line>
</aff>
<aff id="A02">
<institution><![CDATA[,Instituto Nacional de Astrofísica Óptica y Electrónica  ]]></institution>
<addr-line><![CDATA[ Puebla]]></addr-line>
</aff>
<aff id="A03">
<institution><![CDATA[,Instituto de Cibernética, Matemáticas y Física  ]]></institution>
<addr-line><![CDATA[Ciudad de la Habana ]]></addr-line>
<country>Cuba</country>
</aff>
<aff id="A04">
<institution><![CDATA[,IPN Centro de Investigación en Computación ]]></institution>
<addr-line><![CDATA[México D. F.]]></addr-line>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2006</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2006</year>
</pub-date>
<volume>9</volume>
<numero>4</numero>
<fpage>370</fpage>
<lpage>379</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S1405-55462006000200007&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S1405-55462006000200007&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S1405-55462006000200007&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[There is presently no unified methodology that allows the evaluation of supervised or non-supervised classification algorithms. Supervised problems are evaluated through quality functions while non-supervised problems are evaluated through several structural indexes. In both cases a lot of useful information remains hidden or is not considered by the evaluation method, such as the quality of the sample or the structural change generated by the classification algorithm. This work proposes a unified methodology that can be used to evaluate both type of classification problems. This new methodology yields a larger amount of information to the evaluator regarding the quality of the initial sample, when it exists, and regarding the change produced by the classification algorithm in the case of non-supervised classification problems. It also offers the added possibility of making comparative evaluations with different algorithms.]]></p></abstract>
<abstract abstract-type="short" xml:lang="es"><p><![CDATA[Actualmente no existe una metodología que permita la evaluación de algoritmos de clasificación tanto supervisados como no-supervisados. Los algoritmos aplicados a problemas supervisados se evalúan mediante funciones de calidad mientras que los algoritmos aplicados a problemas no-supervisados se evalúan mediante diversos índices estructurales. En ambos casos mucha información útil permanece oculta o no es considerada por el método de evaluación. En este trabajo se propone una metodología unificada que puede ser usada para evaluar ambos tipos de problemas de clasificación. Esta nueva metodología entrega una mayor cantidad de información al evaluador acerca de la calidad de la muestra inicial, cuando ésta existe y acerca de el cambio producido por el algoritmo de clasificación en el caso de problemas no-supervisados. También ofrece la posibilidad de realizar evaluaciones comparativas con diferentes algoritmos.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Supervised Classification]]></kwd>
<kwd lng="en"><![CDATA[Non-Supervised Classification]]></kwd>
<kwd lng="en"><![CDATA[Evaluation of algorithms]]></kwd>
<kwd lng="en"><![CDATA[Methodologies]]></kwd>
<kwd lng="es"><![CDATA[Clasificación Supervisada]]></kwd>
<kwd lng="es"><![CDATA[Clasificación No-Supervisada]]></kwd>
<kwd lng="es"><![CDATA[valuación de algoritmos]]></kwd>
<kwd lng="es"><![CDATA[Metodologías]]></kwd>
</kwd-group>
</article-meta>
</front><body><![CDATA[ <p align="justify"><font face="verdana" size="4">Resumen de tesis doctoral</font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="center"><font face="verdana" size="4"><b>A Unified Methodology to Evaluate Supervised and Non&#150;Supervised Classification Algorithms</b></font></p>     <p align="center"><font face="verdana" size="2">&nbsp;</font></p>     <p align="center"><font face="verdana" size="4"><i>Una Metodolog&iacute;a Unificada para la Evaluaci&oacute;n de Algoritmos de Clasificaci&oacute;n tanto </i><i>Supervisados como No&#150;Supervisados</i></font></p>     <p align="center"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2"><b>Graduated: Salvador Godoy Calder&oacute;n    <br> </b><i>Centro de Investigaci&oacute;n en Computaci&oacute;n&#150;IPN    <br> Av. Juan de Dios B&aacute;tiz s/n esq. Miguel Oth&oacute;n Mendiz&aacute;bal C. P. 07738 M&eacute;xico D. F.</i>    <br> <a href="mailto:sgodoyc@cic.ipn.mx">sgodoyc@cic.ipn.mx    ]]></body>
<body><![CDATA[<br> </a><u>Graduated in june 19, 2006</u></font></p>     <p align="justify"><font face="verdana" size="2"><b>Advisor: Jos&eacute; Francisco Mart&iacute;nez Trinidad    <br> </b><i>Instituto Nacional de Astrof&iacute;sica &Oacute;ptica y Electr&oacute;nica    <br> Luis Enrique Erro 1, Sta. Ma. Tonantzintla, 72840 Puebla</i>    <br> <a href="mailto:fmartine@inaoep.mx">fmartine@inaoep.mx</a></font></p>     <p align="justify"><font face="verdana" size="2"><b>Co&#150;Advisor Manuel S. Lazo&#150;Cortes    <br> </b><i>Instituto de Cibern&eacute;tica, Matem&aacute;ticas y F&iacute;sica    <br> Ministerio de Ciencia, Tecnolog&iacute;a y Medio Ambiente    <br> E No. 309 esq. A 15 Vedado    <br> Ciudad de la Habana, Cuba C. P. 10400</i>    ]]></body>
<body><![CDATA[<br> <a href="mailto:mlazo@icmf.inf.cu">mlazo@icmf.inf.cu</a></font></p>     <p align="justify"><font face="verdana" size="2"><b>Co&#150;Advisor Juan Luis D&iacute;az de Le&oacute;n Santiago    <br> </b><i>Centro de Investigaci&oacute;n en Computaci&oacute;n&#150;IPN    <br> Av. Juan de Dios B&aacute;tiz s/n esq. Miguel Oth&oacute;n Mendiz&aacute;bal C. P. 07738 M&eacute;xico D. F.</i>    <br> <a href="mailto:jdiaz@cic.ipn.mx">jdiaz@cic.ipn.mx</a></font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2"><b>Abstract</b></font></p>     <p align="justify"><font face="verdana" size="2">There is presently no unified methodology that allows the evaluation of supervised or non&#150;supervised classification algorithms. Supervised problems are evaluated through quality functions while non&#150;supervised problems are evaluated through several structural indexes. In both cases a lot of useful information remains hidden or is not considered by the evaluation method, such as the quality of the sample or the structural change generated by the classification algorithm. This work proposes a unified methodology that can be used to evaluate both type of classification problems. This new methodology yields a larger amount of information to the evaluator regarding the quality of the initial sample, when it exists, and regarding the change produced by the classification algorithm in the case of non&#150;supervised classification problems. It also offers the added possibility of making comparative evaluations with different algorithms.</font></p>     <p align="justify"><font face="verdana" size="2"><b>Keywords: </b>Supervised Classification, Non&#150;Supervised Classification, Evaluation of algorithms, Methodologies.</font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     ]]></body>
<body><![CDATA[<p align="justify"><font face="verdana" size="2"><b>Resumen</b></font></p>     <p align="justify"><font face="verdana" size="2">Actualmente no existe una metodolog&iacute;a que permita la evaluaci&oacute;n de algoritmos de clasificaci&oacute;n tanto supervisados como no&#150;supervisados. Los algoritmos aplicados a problemas supervisados se eval&uacute;an mediante funciones de calidad mientras que los algoritmos aplicados a problemas no&#150;supervisados se eval&uacute;an mediante diversos &iacute;ndices estructurales. En ambos casos mucha informaci&oacute;n &uacute;til permanece oculta o no es considerada por el m&eacute;todo de evaluaci&oacute;n. En este trabajo se propone una metodolog&iacute;a unificada que puede ser usada para evaluar ambos tipos de problemas de clasificaci&oacute;n. Esta nueva metodolog&iacute;a entrega una mayor cantidad de informaci&oacute;n al evaluador acerca de la calidad de la muestra inicial, cuando &eacute;sta existe y acerca de el cambio producido por el algoritmo de clasificaci&oacute;n en el caso de problemas no&#150;supervisados. Tambi&eacute;n ofrece la posibilidad de realizar evaluaciones comparativas con diferentes algoritmos.</font></p>     <p align="justify"><font face="verdana" size="2"><b>Palabras   Claves:</b>    Clasificaci&oacute;n   Supervisada,   Clasificaci&oacute;n   No&#150;Supervisada,   Evaluaci&oacute;n   de   algoritmos, Metodolog&iacute;as.</font></p>     <p align="justify">&nbsp;</p>     <p align="justify"><font face="verdana" size="2"><a href="/pdf/cys/v9n4/v9n4a7.pdf" target="_blank">DESCARGA ARTICULO EN FORMATO PDF</a></font></p>     <p align="justify"><font face="verdana" size="2">&nbsp;</font></p>     <p align="justify"><font face="verdana" size="2"><b>References</b></font></p>     <!-- ref --><p align="justify"><font face="verdana" size="2">1. <i>Pattern Recognition. Concepts, Methods and Applications </i>Springer, Portugal, 2001.</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=2040778&pid=S1405-5546200600020000700001&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">2. J. Ruiz Shulcloper, and M. A. Abidi. <i>Logical Combinatorial Pattern Recognition: A Review. </i>Recent Research Developments in Pattern Recognition, Pub. Transword Research Networks, USA, 2002, 133&#150;176.</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=2040779&pid=S1405-5546200600020000700002&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">3. J. Ruiz Shulcloper, Eduardo A. Cabrera, Manuel Lazo Cort&eacute;s <i>Introducci&oacute;n al Reconocimiento de Patrones (Enfoque L&oacute;gico&#150;Combinatorio) </i>CINVESTAV&#150;IPN Serie Verde No. 51, M&eacute;xico, 1995.</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=2040780&pid=S1405-5546200600020000700003&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">4. J. F. Mart&iacute;nez&#150;Trinidad, and A. Guzman&#150;Arenas. "The logical combinatorial approach to Pattern Recognition an overview through selected works". <i>Pattern Recognition, </i>34, 4, 2001, 1&#150;11.</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=2040781&pid=S1405-5546200600020000700004&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">5. J.C. Bezdek <i>Pattern Recognition with fuzzy Objective Function Algorithms </i>Plenum Press, NY, 1981.</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=2040782&pid=S1405-5546200600020000700005&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">6. A.K. Jain, R.C. Dubes <i>Algoritms for Clustering </i>Prentice&#150;Hall, Englewood Cliffs, NJ, 1998.</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=2040783&pid=S1405-5546200600020000700006&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">7. A.K. Jain, M.N. Murty, P. J. Flynn "Data Clustering: a review" <i>ACM Computing Surveys, </i>31(3), 1999.</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=2040784&pid=S1405-5546200600020000700007&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">8. J.C. Bezdek "Numerical taxonomy with fuzzy sets" <i>Journal of Mathematical Biology, </i>1, 1974.</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=2040785&pid=S1405-5546200600020000700008&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">9. J.C. Bezdek "Cluster validity with fuzzy sets" <i>Journal of Cybernetics, 3, 1974.</i></font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=2040786&pid=S1405-5546200600020000700009&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">10. X.L. Xie,   G. Beni "A validity measure for fuzzy clustering" <i>IEEE Transactions on Pattern An&aacute;lisis and Machine Inteligence, </i>13(8), 1991.</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=2040787&pid=S1405-5546200600020000700010&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">11. M. Lazo&#150;Cort&eacute;s "Models based on Testor theory for feature selection and supervised classification with non classical object descriptions" PhD. Tesis, Universidad Central de las Villas, Cuba, 1994. (In Spanish)</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=2040788&pid=S1405-5546200600020000700011&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">12. S. Godoy&#150;Calder&oacute;n, M. Lazo&#150;Cort&eacute;s, J.F. Mart&iacute;nez&#150;Trinidad "A non&#150;classical view of Coverings and its implications in the formalization of Pattern Recognition problems" <i>WSEAS Transactions on Mathematics, 2, 1&#150;2, </i>2003, 60&#150;66.</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=2040789&pid=S1405-5546200600020000700012&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">13. Dae&#150;Won Kim, Kwang H. Lee, Doheon Lee "On cluster validity index for estimation of the optimal number of fuzzy clusters" <i>Pattern Recognition </i>37, 2004.</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=2040790&pid=S1405-5546200600020000700013&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --><!-- ref --><p align="justify"><font face="verdana" size="2">14. H. Lee&#150;Kwang, Y.S. Song, K.M. Lee "Similarity measure between fuzzy sets and between elements" <i>Fuzzy Sets and Systems </i>62, 1994.</font>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;[&#160;<a href="javascript:void(0);" onclick="javascript: window.open('/scielo.php?script=sci_nlinks&ref=2040791&pid=S1405-5546200600020000700014&lng=','','width=640,height=500,resizable=yes,scrollbars=1,menubar=yes,');">Links</a>&#160;]<!-- end-ref --> ]]></body><back>
<ref-list>
<ref id="B1">
<label>1</label><nlm-citation citation-type="book">
<source><![CDATA[Pattern Recognition: Concepts, Methods and Applications]]></source>
<year>2001</year>
<publisher-name><![CDATA[Springer]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B2">
<label>2</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ruiz Shulcloper]]></surname>
<given-names><![CDATA[J]]></given-names>
</name>
<name>
<surname><![CDATA[Abidi]]></surname>
<given-names><![CDATA[M. A]]></given-names>
</name>
</person-group>
<source><![CDATA[Logical Combinatorial Pattern Recognition: A Review]]></source>
<year>2002</year>
<page-range>133-176</page-range><publisher-name><![CDATA[Pub. Transword Research Networks]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B3">
<label>3</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ruiz Shulcloper]]></surname>
<given-names><![CDATA[J]]></given-names>
</name>
<name>
<surname><![CDATA[Cabrera]]></surname>
<given-names><![CDATA[Eduardo A]]></given-names>
</name>
<name>
<surname><![CDATA[Lazo Cortés]]></surname>
<given-names><![CDATA[Manuel]]></given-names>
</name>
</person-group>
<source><![CDATA[Introducción al Reconocimiento de Patrones (Enfoque Lógico-Combinatorio)]]></source>
<year>1995</year>
<publisher-name><![CDATA[CINVESTAV-IPN]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B4">
<label>4</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Martínez-Trinidad]]></surname>
<given-names><![CDATA[J. F]]></given-names>
</name>
<name>
<surname><![CDATA[Guzman-Arenas]]></surname>
<given-names><![CDATA[A]]></given-names>
</name>
</person-group>
<article-title xml:lang="en"><![CDATA[The logical combinatorial approach to Pattern Recognition an overview through selected works]]></article-title>
<source><![CDATA[Pattern Recognition]]></source>
<year>2001</year>
<volume>34</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>1-11</page-range></nlm-citation>
</ref>
<ref id="B5">
<label>5</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bezdek]]></surname>
<given-names><![CDATA[J.C]]></given-names>
</name>
</person-group>
<source><![CDATA[Pattern Recognition with fuzzy Objective Function Algorithms]]></source>
<year>1981</year>
<publisher-loc><![CDATA[^eNY NY]]></publisher-loc>
<publisher-name><![CDATA[Plenum Press]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B6">
<label>6</label><nlm-citation citation-type="book">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Jain]]></surname>
<given-names><![CDATA[A.K]]></given-names>
</name>
<name>
<surname><![CDATA[Dubes]]></surname>
<given-names><![CDATA[R.C]]></given-names>
</name>
</person-group>
<source><![CDATA[Algoritms for Clustering]]></source>
<year>1998</year>
<publisher-loc><![CDATA[Englewood Cliffs^eNJ NJ]]></publisher-loc>
<publisher-name><![CDATA[Prentice-Hall]]></publisher-name>
</nlm-citation>
</ref>
<ref id="B7">
<label>7</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Jain]]></surname>
<given-names><![CDATA[A.K]]></given-names>
</name>
<name>
<surname><![CDATA[Murty]]></surname>
<given-names><![CDATA[M.N]]></given-names>
</name>
<name>
<surname><![CDATA[Flynn]]></surname>
<given-names><![CDATA[P. J]]></given-names>
</name>
</person-group>
<article-title xml:lang="en"><![CDATA[Data Clustering: a review]]></article-title>
<source><![CDATA[ACM Computing Surveys]]></source>
<year>1999</year>
<volume>31</volume>
<numero>3</numero>
<issue>3</issue>
</nlm-citation>
</ref>
<ref id="B8">
<label>8</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bezdek]]></surname>
<given-names><![CDATA[J.C]]></given-names>
</name>
</person-group>
<article-title xml:lang="en"><![CDATA[Numerical taxonomy with fuzzy sets]]></article-title>
<source><![CDATA[Journal of Mathematical Biology]]></source>
<year>1974</year>
<numero>1</numero>
<issue>1</issue>
</nlm-citation>
</ref>
<ref id="B9">
<label>9</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Bezdek]]></surname>
<given-names><![CDATA[J.C]]></given-names>
</name>
</person-group>
<article-title xml:lang="en"><![CDATA[Cluster validity with fuzzy sets]]></article-title>
<source><![CDATA[Journal of Cybernetics]]></source>
<year>1974</year>
<numero>3</numero>
<issue>3</issue>
</nlm-citation>
</ref>
<ref id="B10">
<label>10</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Xie]]></surname>
<given-names><![CDATA[X.L]]></given-names>
</name>
<name>
<surname><![CDATA[Beni]]></surname>
<given-names><![CDATA[G]]></given-names>
</name>
</person-group>
<article-title xml:lang="en"><![CDATA[A validity measure for fuzzy clustering]]></article-title>
<source><![CDATA[IEEE Transactions on Pattern Análisis and Machine Inteligence]]></source>
<year>1991</year>
<volume>13</volume>
<numero>8</numero>
<issue>8</issue>
</nlm-citation>
</ref>
<ref id="B11">
<label>11</label><nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lazo-Cortés]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
</person-group>
<source><![CDATA[Models based on Testor theory for feature selection and supervised classification with non classical object descriptions]]></source>
<year></year>
</nlm-citation>
</ref>
<ref id="B12">
<label>12</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Godoy-Calderón]]></surname>
<given-names><![CDATA[S]]></given-names>
</name>
<name>
<surname><![CDATA[Lazo-Cortés]]></surname>
<given-names><![CDATA[M]]></given-names>
</name>
<name>
<surname><![CDATA[Martínez-Trinidad]]></surname>
<given-names><![CDATA[J.F]]></given-names>
</name>
</person-group>
<article-title xml:lang="en"><![CDATA[A non-classical view of Coverings and its implications in the formalization of Pattern Recognition problems]]></article-title>
<source><![CDATA[WSEAS Transactions on Mathematics]]></source>
<year>2003</year>
<volume>2</volume>
<numero>1-2</numero>
<issue>1-2</issue>
<page-range>60-66</page-range></nlm-citation>
</ref>
<ref id="B13">
<label>13</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Kim]]></surname>
<given-names><![CDATA[Dae-Won]]></given-names>
</name>
<name>
<surname><![CDATA[Lee]]></surname>
<given-names><![CDATA[Kwang H]]></given-names>
</name>
<name>
<surname><![CDATA[Lee]]></surname>
<given-names><![CDATA[Doheon]]></given-names>
</name>
</person-group>
<article-title xml:lang="en"><![CDATA[On cluster validity index for estimation of the optimal number of fuzzy clusters]]></article-title>
<source><![CDATA[Pattern Recognition]]></source>
<year>2004</year>
<numero>37</numero>
<issue>37</issue>
</nlm-citation>
</ref>
<ref id="B14">
<label>14</label><nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Lee-Kwang]]></surname>
<given-names><![CDATA[H]]></given-names>
</name>
<name>
<surname><![CDATA[Song]]></surname>
<given-names><![CDATA[Y.S]]></given-names>
</name>
<name>
<surname><![CDATA[Lee]]></surname>
<given-names><![CDATA[K.M]]></given-names>
</name>
</person-group>
<article-title xml:lang="en"><![CDATA[Similarity measure between fuzzy sets and between elements]]></article-title>
<source><![CDATA[Fuzzy Sets and Systems]]></source>
<year>1994</year>
<numero>62</numero>
<issue>62</issue>
</nlm-citation>
</ref>
</ref-list>
</back>
</article>
