https://www.gphjournal.org/index.php/m/issue/feedGPH-International Journal of Mathematics2025-09-29T10:03:02+00:00Dr. EKEKE, JOHN NDUBUEZEdrekekejohn@gmail.comOpen Journal Systems<p style="font-family: 'Segoe UI', sans-serif; font-size: 16px; color: #333;"><strong>GPH-International Journal of Mathematics (e-ISSN <a href="https://portal.issn.org/resource/ISSN/3050-9629" target="_blank" rel="noopener">3050-9645</a>)</strong> is a peer-reviewed, open-access journal dedicated to advancing research in mathematics. The journal publishes original research articles, comprehensive reviews, and survey papers covering both pure and applied mathematics, including topics such as algebra, analysis, geometry, number theory, and mathematical modeling. It provides a global platform for mathematicians and researchers to share innovative ideas, foster interdisciplinary collaboration, and contribute to the advancement of mathematical knowledge.</p>https://www.gphjournal.org/index.php/m/article/view/2105ON THE STRUCTURE OF TWO - FOLD FUZZY SET2025-09-29T10:03:02+00:00Naphtali B Jeltenjeltenn2012@gmail.comLois A. Ademolanoreplygphjournals@gmail.comDachollom Sambonoreplygphjournals@gmail.comMusaddid Abdulkareem Dayyibnoreplygphjournals@gmail.comAudu Bubanoreplygphjournals@gmail.com<p>The traditional fuzzy set deals with single degree of membership which cannot capture matters exhibited by multi-dimensional uncertainty. This gap motivate is the motivation to our work. We extend the existing Boolean algebra of the traditional fuzzy set to the two-fold fuzzy set., to further make its application wider and easier. The results show the conformity of the two-fold fuzzy sets with the existing Boolean algebra in the theory of the traditional fuzzy sets. The basic operations of the traditional fuzzy set were investigated against the two-fold fuzzy sets. The axioms of fuzzy union, fuzzy intersection and fuzzy complement of the traditional fuzzy set were investigated and extended to that of the two-fold fuzzy set. Furthermore, the set having satisfied the axioms was proved to be commutative, associative, distributive, involutivity, absorptive point-wise, and in concord with De Morgan’s law. With this the two fold fuzzy set will be more relevant in modelling vagueness and imprecision than the traditional fuzzy set.</p>2025-09-29T10:03:02+00:00##submission.copyrightStatement##