<?xml version="1.0" encoding="UTF-8"?>
<article article-type="Research Article">
  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher">journal-of-discrete-mathematical-sciences-and-cryptography</journal-id>
      <journal-title-group>
        <journal-title>Journal of Discrete Mathematical Sciences and Cryptography</journal-title>
      </journal-title-group>
      <issn publication-format="electronic">2169-0065</issn>
      <issn publication-format="print">0972-0529</issn>
      <publisher>
        <publisher-name>Taru Publications</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.47974/JDMSC-1835</article-id>
      <title-group>
        <article-title>Inverse n-dominating sets in vague graphs with application in decision making</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author">
          <name>
            <surname>Banitalebi</surname>
            <given-names>S.</given-names>
          </name>
          <aff>Department of Cognitive Modeling and Simulation, Faculty of Artificial Intelligence and Cognitive Sciences, Imam Hossein University, Tehran, 1698715861, Iran</aff>
        </contrib>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Borzooei</surname>
            <given-names>R. A.</given-names>
          </name>
          <aff>Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, 1983969411, Iran</aff>
          <aff>Department of Mathematics, Faculty of Engineering and Natural Sciences, Istinye University, Istanbul, Turkiye</aff>
        </contrib>
      </contrib-group>
      <volume>28</volume>
      <issue>1</issue>
      <fpage>61</fpage>
      <lpage>76</lpage>
      <pub-date date-type="pub">
        <day>28</day>
        <month>02</month>
        <year>2025</year>
      </pub-date>
      <abstract>
        <p>Compared to other graph models, vague graph models are more compatible and flexible in modeling situations with imprecise information.The goal of thise study is to introduce the nations of inverse vague-dominating set, inverse vague-domination numbers and some of their properties in vague graphs. Eventually, the researchers have been provided an application that can be used to locate aid centers. </p>
      </abstract>
      <kwd-group>
        <kwd>Vague graph</kwd>
        <kwd>Inverse vague-dominating set</kwd>
        <kwd>Inverse vague-domination number</kwd>
      </kwd-group>
      <custom-meta-group>
        <custom-meta>
          <meta-name>access</meta-name>
          <meta-value>open</meta-value>
        </custom-meta>
        <custom-meta>
          <meta-name>retracted</meta-name>
          <meta-value>no</meta-value>
        </custom-meta>
      </custom-meta-group>
    </article-meta>
  </front>
</article>
