<?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>S1405-55462021000400775</article-id>
<article-id pub-id-type="doi">10.13053/cys-25-4-4094</article-id>
<title-group>
<article-title xml:lang="en"><![CDATA[Negations of Probability Distributions: A Survey]]></article-title>
</title-group>
<contrib-group>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Batyrshin]]></surname>
<given-names><![CDATA[Ildar Z.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Kubysheva]]></surname>
<given-names><![CDATA[Nailya I.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Bayrasheva]]></surname>
<given-names><![CDATA[Venera R.]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Kosheleva]]></surname>
<given-names><![CDATA[Olga]]></given-names>
</name>
<xref ref-type="aff" rid="Aff"/>
</contrib>
<contrib contrib-type="author">
<name>
<surname><![CDATA[Kreinovich]]></surname>
<given-names><![CDATA[Vladik]]></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[Mexico City ]]></addr-line>
<country>Mexico</country>
</aff>
<aff id="Af2">
<institution><![CDATA[,Kazan Federal University  ]]></institution>
<addr-line><![CDATA[Kazan ]]></addr-line>
<country>Russia</country>
</aff>
<aff id="Af3">
<institution><![CDATA[,University of Texas  ]]></institution>
<addr-line><![CDATA[El Paso ]]></addr-line>
<country>USA</country>
</aff>
<pub-date pub-type="pub">
<day>00</day>
<month>12</month>
<year>2021</year>
</pub-date>
<pub-date pub-type="epub">
<day>00</day>
<month>12</month>
<year>2021</year>
</pub-date>
<volume>25</volume>
<numero>4</numero>
<fpage>775</fpage>
<lpage>781</lpage>
<copyright-statement/>
<copyright-year/>
<self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_arttext&amp;pid=S1405-55462021000400775&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_abstract&amp;pid=S1405-55462021000400775&amp;lng=en&amp;nrm=iso"></self-uri><self-uri xlink:href="http://www.scielo.org.mx/scielo.php?script=sci_pdf&amp;pid=S1405-55462021000400775&amp;lng=en&amp;nrm=iso"></self-uri><abstract abstract-type="short" xml:lang="en"><p><![CDATA[Abstract: In recent years many papers have been devoted to the analysis and applications of negations of finite probability distributions (PD), first considered by Ronald Yager. This paper gives a brief overview of some formal results on the definition and properties of negations of PD. Negations of PD are generated by negators of probability values transforming element-by-element PD into a negation of PD. Negators are non-increasing functions of probability values. There are two types of negators: PD-independent and PD-dependent negators. Yager's negator is fundamental in the characterization of linear PD-independent negators as a convex combination of Yager's negator and uniform negator. Involutivity of negations is important in logic, and such involutive negator is considered in the paper. We propose a new simple definition of the class of linear negators generalizing Yager's negator. Different examples illustrate properties of negations of PD. Finally, we consider some open problems in the analysis of negations of probability distributions.]]></p></abstract>
<kwd-group>
<kwd lng="en"><![CDATA[Probability distribution]]></kwd>
<kwd lng="en"><![CDATA[negation]]></kwd>
<kwd lng="en"><![CDATA[linear negator]]></kwd>
<kwd lng="en"><![CDATA[involutive negation]]></kwd>
</kwd-group>
</article-meta>
</front><back>
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