<?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>S1405-55462024000200701</article-id>
<article-id pub-id-type="doi">10.13053/cys-28-2-5049</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Analysis of Relationships between Co-Symmetric Dissimilarity Measures of Probability Distributions with Involutive Negations]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Ensástegui-Ortega]]></surname>
<given-names><![CDATA[María Elena]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Batyrshin]]></surname>
<given-names><![CDATA[Ildar]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Gelbukh]]></surname>
<given-names><![CDATA[Alexander]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Kubysheva]]></surname>
<given-names><![CDATA[Nailya]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
</contrib-group>
<aff id="Af1">
<institution><![CDATA[,Instituto Politécnico Nacional Centro de Investigación en Computación ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Kazan (Volga Region) Federal University  ]]></institution>
<addr-line><![CDATA[ ]]></addr-line>
<country>Republic of Tatarstan, Russia</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>06</month>
<year>2024</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>06</month>
<year>2024</year>
</pub-date>
<volume>28</volume>
<numero>2</numero>
<fpage>701</fpage>
<lpage>707</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S1405-55462024000200701&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S1405-55462024000200701&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S1405-55462024000200701&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract: Learning from data in almost any human activity is a very important task, usually using similarity or dissimilarity between data. Recently, it was shown the importance of considering the involution operation defined on the data domain which reflects a symmetry of data structures. This symmetry should be taken into account in data analysis. Co-symmetric similarity and dissimilarity measures defined over a set with involution play an important role in data analysis. In this paper, four dissimilarity functions over the set of probability distributions are created that meet the property of co-symmetry with respect to the involutive negation of distributions. Scatter graphs are generated from their respective dissimilarity matrices to compare the similarity between them. Additionally, the Pearson, Kendall, and Spearman correlation coefficients are calculated to numerically assess the relationship that exists. Subsequently, four dissimilarity functions are considered due to their higher correlation with those studied in this paper. They are divided into two groups, and an analysis is conducted to determine which are more correlated.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Co-symmetry]]></kwd>
<kwd lng="en"><![CDATA[correlation]]></kwd>
<kwd lng="en"><![CDATA[dissimilarity]]></kwd>
<kwd lng="en"><![CDATA[involution]]></kwd>
<kwd lng="en"><![CDATA[probability distribution]]></kwd>
</kwd-group>
</article-meta>
</front><back>
<ref-list>
<ref id="B1">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Cha]]></surname>
<given-names><![CDATA[S. H.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Comprehensive survey on distance/similarity measures between probability density functions]]></article-title>
<source><![CDATA[International journal of mathematical models and methods in applied sciences]]></source>
<year>2007</year>
<volume>1</volume>
<numero>2</numero>
<issue>2</issue>
<page-range>1-8</page-range></nlm-citation>
</ref>
<ref id="B2">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Sáez]]></surname>
<given-names><![CDATA[C.]]></given-names>
</name>
<name>
<surname><![CDATA[Robles]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[García-Gómez]]></surname>
<given-names><![CDATA[J. M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Stability metrics for multi-source biomedical data based on simplicial projections from probability distribution distances]]></article-title>
<source><![CDATA[Statistical Methods in Medical Research]]></source>
<year>2016</year>
<volume>26</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>312-36</page-range></nlm-citation>
</ref>
<ref id="B3">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Batyrshin]]></surname>
<given-names><![CDATA[I. Z.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Contracting and involutive negations of probability distributions]]></article-title>
<source><![CDATA[Mathematics]]></source>
<year>2021</year>
<volume>9</volume>
<numero>19</numero>
<issue>19</issue>
<page-range>2389</page-range></nlm-citation>
</ref>
<ref id="B4">
<nlm-citation citation-type="">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Rudas]]></surname>
<given-names><![CDATA[I. J.]]></given-names>
</name>
<name>
<surname><![CDATA[Batyrshin]]></surname>
<given-names><![CDATA[I. Z.]]></given-names>
</name>
</person-group>
<source><![CDATA[Explainable correlation of categorical data and bar charts]]></source>
<year>2023</year>
<volume>1</volume>
<page-range>81-8</page-range></nlm-citation>
</ref>
<ref id="B5">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Batyrshin]]></surname>
<given-names><![CDATA[I. Z.]]></given-names>
</name>
<name>
<surname><![CDATA[Rudas]]></surname>
<given-names><![CDATA[I. J.]]></given-names>
</name>
<name>
<surname><![CDATA[Kubysheva]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
<name>
<surname><![CDATA[Akhtyamova]]></surname>
<given-names><![CDATA[S.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Similarity correlation of frequency distributions of categorical data in analysis of cognitive decline severity in asthmatics]]></article-title>
<source><![CDATA[Computación y Sistemas]]></source>
<year>2022</year>
<volume>26</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>1603-9</page-range></nlm-citation>
</ref>
<ref id="B6">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Batyrshin]]></surname>
<given-names><![CDATA[I. Z.]]></given-names>
</name>
<name>
<surname><![CDATA[Tóth-Laufer]]></surname>
<given-names><![CDATA[E.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Bipolar dissimilarity and similarity correlations of numbers]]></article-title>
<source><![CDATA[Mathematics]]></source>
<year>2022</year>
<volume>10</volume>
<numero>5</numero>
<issue>5</issue>
<page-range>797</page-range></nlm-citation>
</ref>
<ref id="B7">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Ensastegui-Ortega]]></surname>
<given-names><![CDATA[M. E.]]></given-names>
</name>
<name>
<surname><![CDATA[Batyrshin]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
<name>
<surname><![CDATA[Cárdenas&#8211;Perez]]></surname>
<given-names><![CDATA[M. F.]]></given-names>
</name>
<name>
<surname><![CDATA[Kubysheva]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
<name>
<surname><![CDATA[Gelbukh]]></surname>
<given-names><![CDATA[A.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Dissimilarity functions co-symmetry property: a focus on probability distributions with involutive negation]]></article-title>
<source><![CDATA[Journal of Intelligent &amp; Fuzzy Systems]]></source>
<year>2024</year>
<page-range>1-10</page-range></nlm-citation>
</ref>
<ref id="B8">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Yager]]></surname>
<given-names><![CDATA[R. R.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[On the maximum entropy negation of a probability distribution]]></article-title>
<source><![CDATA[IEEE Transactions on Fuzzy Systems]]></source>
<year>2015</year>
<volume>23</volume>
<numero>5</numero>
<issue>5</issue>
<page-range>1899-902</page-range></nlm-citation>
</ref>
<ref id="B9">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Batyrshin]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
<name>
<surname><![CDATA[Villa-Vargas]]></surname>
<given-names><![CDATA[L. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Ramírez-Salinas]]></surname>
<given-names><![CDATA[M. A.]]></given-names>
</name>
<name>
<surname><![CDATA[Salinas-Rosales]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Kubysheva]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Generating negations of probability distributions]]></article-title>
<source><![CDATA[Soft Computing]]></source>
<year>2021</year>
<volume>25</volume>
<numero>12</numero>
<issue>12</issue>
<page-range>7929-35</page-range></nlm-citation>
</ref>
<ref id="B10">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Klein]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Some technical remarks on negations of discrete probability distributions and their information loss]]></article-title>
<source><![CDATA[Mathematics]]></source>
<year>2022</year>
<volume>10</volume>
<numero>20</numero>
<issue>20</issue>
<page-range>3893</page-range></nlm-citation>
</ref>
<ref id="B11">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Batyrshin]]></surname>
<given-names><![CDATA[I. Z.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Fuzzy distribution sets]]></article-title>
<source><![CDATA[Computación y Sistemas]]></source>
<year>2022</year>
<volume>26</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>1411-6</page-range></nlm-citation>
</ref>
<ref id="B12">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Batyrshin]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
<name>
<surname><![CDATA[Rudas]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
<name>
<surname><![CDATA[Kubysheva]]></surname>
<given-names><![CDATA[N.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Parametric negations of probability distributions and fuzzy distribution sets]]></article-title>
<source><![CDATA[Computación y Sistemas]]></source>
<year>2023</year>
<volume>27</volume>
<numero>3</numero>
<issue>3</issue>
<page-range>619-25</page-range></nlm-citation>
</ref>
<ref id="B13">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Batyrshin]]></surname>
<given-names><![CDATA[I.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Towards a general theory of similarity and association measures: similarity, dissimilarity and correlation functions]]></article-title>
<source><![CDATA[Journal of Intelligent &amp; Fuzzy Systems]]></source>
<year>2019</year>
<volume>36</volume>
<numero>4</numero>
<issue>4</issue>
<page-range>2977-3004</page-range></nlm-citation>
</ref>
<ref id="B14">
<nlm-citation citation-type="journal">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Batagelj]]></surname>
<given-names><![CDATA[V.]]></given-names>
</name>
<name>
<surname><![CDATA[Bren]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<article-title xml:lang=""><![CDATA[Comparing resemblance measures]]></article-title>
<source><![CDATA[Journal of Classification]]></source>
<year>1995</year>
<volume>12</volume>
<numero>1</numero>
<issue>1</issue>
<page-range>73-90</page-range></nlm-citation>
</ref>
<ref id="B15">
<nlm-citation citation-type="confpro">
<person-group person-group-type="author">
<name>
<surname><![CDATA[Omhover]]></surname>
<given-names><![CDATA[J.]]></given-names>
</name>
<name>
<surname><![CDATA[Rifqi]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
<name>
<surname><![CDATA[Detyniecki]]></surname>
<given-names><![CDATA[M.]]></given-names>
</name>
</person-group>
<source><![CDATA[Ranking invariance based on similarity measures in document retrieval]]></source>
<year>2006</year>
<conf-name><![CDATA[ Adaptive Multimedia Retrieval: User, Context, and Feedback: AMR]]></conf-name>
<conf-date>2005</conf-date>
<conf-loc> </conf-loc>
<page-range>55-64</page-range></nlm-citation>
</ref>
</ref-list>
</back>
</article>
