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All Journal Epsilon: Jurnal Matematika Murni dan Terapan
Moch Idris
Universitas Lambung Mangkurat
Decision Sciences, Operations Research & Management Transportation

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LOWER LEVEL SUBGRUPOID Saman Abdurrahman; Na'imah Hijriati; Thresye Thresye; Moch Idris; Aprida Siska Lestia
EPSILON: JURNAL MATEMATIKA MURNI DAN TERAPAN Vol 19, No 2 (2025)
Publisher : Mathematics Study Program, Faculty of Mathematics and Natural Sciences, Lambung Mangkurat

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.20527/epsilon.v19i2.15332

Abstract

This study investigates the structure of anti-fuzzy subgroupoids within the framework of groupoids, extending the theory of fuzzy subgroups beyond traditional group-based algebraic systems. While numerous fuzzy approaches have been applied to groups and semigroups, the exploration of groupoids algebraic structures without the necessity of identity or inverse elements remains limited, particularly in the context of anti-fuzzy theory. This research addresses that gap by developing a mathematical characterization of anti-fuzzy subgroupoids and systematically analyzing their relationship with lower-level subsets. A key result demonstrates that every subgroupoid can be represented as a lower-level subset of a suitably constructed anti-fuzzy subgroupoid. Furthermore, it is shown that equality of two lower-level subsets occurs if and only if no element exists with a membership value strictly between the corresponding thresholds. Employing a deductive and axiomatic approach, this work contributes to the theoretical advancement of fuzzy structures in non-classical algebra. It offers a foundation for future applications in uncertainty-based decision systems
Co-Authors Aprida Siska Lestia Hijriati, Naimah Saman Abdurrahman Thresye Thresye