<?xml version="1.0" encoding="UTF-8"?>
<article article-type="A">
  <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">10.1080/09720529.2021.1938985</article-id>
      <title-group>
        <article-title>Norms over bifuzzy submodules</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, Tehran, Payame Noor University (PNU), Iran</aff>
        </contrib>
      </contrib-group>
      <volume>26</volume>
      <issue>2</issue>
      <fpage>359</fpage>
      <lpage>376</lpage>
      <pub-date date-type="pub">
        <day>23</day>
        <month>02</month>
        <year>2022</year>
      </pub-date>
      <abstract>
        <p>In this work, we introduce the concepts of bifuzzy submodules under norms and consider some of their properties and structured characteristics. Also, we investigate the intersection and direct product of them and obtaion some new results. Finally, we investigate their properties under homomorphisms of modules.</p>
      </abstract>
      <kwd-group>
        <kwd>Fuzzy set theory</kwd>
        <kwd>Bifuzzy set</kwd>
        <kwd>Norms</kwd>
        <kwd>Modules</kwd>
        <kwd>Products and intersections</kwd>
        <kwd>Morphisms</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>
