<?xml version="1.0" encoding="UTF-8"?>
<article article-type="Research Article">
  <front>
    <journal-meta>
      <journal-id journal-id-type="publisher">journal-of-information-and-optimization-sciences</journal-id>
      <journal-title-group>
        <journal-title>Journal of Information and Optimization Sciences</journal-title>
      </journal-title-group>
      <issn publication-format="electronic">2169-0103</issn>
      <issn publication-format="print">0252-2667</issn>
      <publisher>
        <publisher-name>Taru Publications</publisher-name>
      </publisher>
    </journal-meta>
    <article-meta>
      <article-id pub-id-type="doi">10.47974/JIOS-1422</article-id>
      <title-group>
        <article-title>Intuitionistic fuzzy equivalence relations and ideals on rings under norms</article-title>
      </title-group>
      <contrib-group>
        <contrib contrib-type="author" corresp="yes">
          <name>
            <surname>Rasuli</surname>
            <given-names>Rasul</given-names>
          </name>
          <aff>Department of Mathematics, Payame Noor University (PNU), Tehran, P. O. Box 19395-4697, Iran</aff>
        </contrib>
      </contrib-group>
      <volume>47</volume>
      <issue>4</issue>
      <fpage>1301</fpage>
      <lpage>1312</lpage>
      <pub-date date-type="pub">
        <day>03</day>
        <month>10</month>
        <year>2025</year>
      </pub-date>
      <abstract>
        <p>In this paper, we investigate norms defined on intuitionistic fuzzy equivalence relations, intuitionistic fuzzy congruence relations, and intuitionistic fuzzy ideals of rings. We explore their properties and structural characteristics, as well as their behavior under ring homomorphisms.</p>
      </abstract>
      <kwd-group>
        <kwd>General commutative ring theory</kwd>
        <kwd>Theory of fuzzy sets</kwd>
        <kwd>Congruence relations</kwd>
        <kwd>Intuitionistic fuzzy equivalence relations</kwd>
        <kwd>Intuitionistic fuzzy congruence relations</kwd>
        <kwd>Intuitionistic fuzzy ideals</kwd>
        <kwd>Norms</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>
