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Jurnal
Fuzzy Ideal and Fuzzy Filter on Ordered Groupoid
Jurnal Matematika, Statistika dan Komputasi
ISSN 2614-8811, 1858-1382
Published 2026-09-15
Publisher Department of Mathematics, Hasanuddin University
Language en
Abstract
Within fuzzy set theory, every element of nonempty set is assigned membership degree in interval [0, 1]. With development of fuzzy set theory, its concepts have been extended to algebraic structures, including ordered groupoids, leading to investigation of fuzzy ideals and fuzzy filters. This research investigates properties of fuzzy ideals together with their correspondence to classical ideals through fuzzy membership functions. It also studies the characteristics of fuzzy filters and their connection with fuzzy prime ideals. This research uses literature review to examine relationship between classical ideals and fuzzy ideals in ordered groupoids and by proving conditions for fuzzy subset to be a fuzzy ideal. Analysis also includes the characterization of fuzzy filters and their relation to fuzzy prime ideals through concept of fuzzy subset complements. The findings reveal that the characteristic function induced by a nonempty subset forms a fuzzy ideal precisely when the subset itself is an ideal of the ordered groupoid. Therefore, fuzzy ideals provide a natural generalization of classical ideals while maintaining the ordering relation and binary operation defined on an ordered groupoid.
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Metadata source: OAI-PMH (metadata jurnal) https://journal.unhas.ac.id/index.php/jmsk/oai,
first harvested 5 Nov 2026,
last seen 5 Nov 2026.
Original metadata (oai_dc)
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<dc:title xml:lang="en">Fuzzy Ideal and Fuzzy Filter on Ordered Groupoid </dc:title>
<dc:creator xml:lang="en">Muliawati, Aminah</dc:creator>
<dc:creator xml:lang="en">Abdurrahman, Saman</dc:creator>
<dc:creator xml:lang="en">Thresye, Thresye</dc:creator>
<dc:subject xml:lang="en">Ordered Groupoid</dc:subject>
<dc:subject xml:lang="en">Fuzzy Ideal</dc:subject>
<dc:subject xml:lang="en">Fuzzy Filter</dc:subject>
<dc:subject xml:lang="en">Fuzzy Membership Function</dc:subject>
<dc:subject xml:lang="en">Fuzzy Prime Ideal</dc:subject>
<dc:subject xml:lang="en">Fuzzy Set Theory</dc:subject>
<dc:subject xml:lang="en">Algebra</dc:subject>
<dc:subject xml:lang="en">Abstract Algebra</dc:subject>
<dc:subject xml:lang="en">Ordered Groupoids</dc:subject>
<dc:subject xml:lang="en">Fuzzy Algebra</dc:subject>
<dc:subject xml:lang="en">Algebraic Structures</dc:subject>
<dc:subject xml:lang="en">Mathematical Logic</dc:subject>
<dc:subject xml:lang="en">Pure Mathematics</dc:subject>
<dc:subject xml:lang="en">Ordered Algebraic Structures</dc:subject>
<dc:subject xml:lang="en">Fuzzy Mathematics</dc:subject>
<dc:description xml:lang="en">Within fuzzy set theory, every element of nonempty set is assigned membership degree in interval [0, 1]. With development of fuzzy set theory, its concepts have been extended to algebraic structures, including ordered groupoids, leading to investigation of fuzzy ideals and fuzzy filters. This research investigates properties of fuzzy ideals together with their correspondence to classical ideals through fuzzy membership functions. It also studies the characteristics of fuzzy filters and their connection with fuzzy prime ideals. This research uses literature review to examine relationship between classical ideals and fuzzy ideals in ordered groupoids and by proving conditions for fuzzy subset to be a fuzzy ideal. Analysis also includes the characterization of fuzzy filters and their relation to fuzzy prime ideals through concept of fuzzy subset complements. The findings reveal that the characteristic function induced by a nonempty subset forms a fuzzy ideal precisely when the subset itself is an ideal of the ordered groupoid. Therefore, fuzzy ideals provide a natural generalization of classical ideals while maintaining the ordering relation and binary operation defined on an ordered groupoid.</dc:description>
<dc:publisher xml:lang="en">Department of Mathematics, Hasanuddin University</dc:publisher>
<dc:date>2026-09-15</dc:date>
<dc:type>info:eu-repo/semantics/article</dc:type>
<dc:type>info:eu-repo/semantics/publishedVersion</dc:type>
<dc:type xml:lang="en">text</dc:type>
<dc:format>application/pdf</dc:format>
<dc:identifier>https://journal.unhas.ac.id/index.php/jmsk/article/view/53141</dc:identifier>
<dc:identifier>10.20956/912h0e65</dc:identifier>
<dc:source xml:lang="en">Jurnal Matematika, Statistika dan Komputasi; Vol. 23 No. 1 (2026): September 2026; 236-245</dc:source>
<dc:source>2614-8811</dc:source>
<dc:source>1858-1382</dc:source>
<dc:language>en</dc:language>
<dc:relation>https://journal.unhas.ac.id/index.php/jmsk/article/view/53141/15018</dc:relation>
<dc:coverage xml:lang="en">This research investigates fuzzy ideals and fuzzy filters on ordered groupoids using literature review and mathematical proofs, focusing on their characterization and their relationships with classical ideals and fuzzy prime ideals.</dc:coverage>
<dc:rights xml:lang="en">Copyright (c) 2026 Jurnal Matematika, Statistika dan Komputasi</dc:rights>
<dc:rights xml:lang="en">https://creativecommons.org/licenses/by/4.0</dc:rights>
</oai_dc:dc>
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APA 7
Muliawati, A., Abdurrahman, S., & Thresye, T. (2026). Fuzzy Ideal and Fuzzy Filter on Ordered Groupoid. Jurnal Matematika, Statistika dan Komputasi, 23(1), 236–245. https://doi.org/10.20956/912h0e65
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IEEE
A. Muliawati, S. Abdurrahman, and T. Thresye, “Fuzzy Ideal and Fuzzy Filter on Ordered Groupoid,” Jurnal Matematika, Statistika dan Komputasi, vol. 23, no. 1, pp. 236–245, 2026, doi: 10.20956/912h0e65.
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