SIFAT SUBGRUP NORMAL DARI ANTI SUBGRUP NORMAL FUZZY

Cendikia Hira; Saman Abdurrahman; Thresye Thresye

doi:10.20527/epsilon.v17i1.9135

SIFAT SUBGRUP NORMAL DARI ANTI SUBGRUP NORMAL FUZZY

Cendikia Hira, Saman Abdurrahman, Thresye Thresye

Abstract

A fuzzy set is a concept theory that provide a solution of problem that cannot be explained by crisp set. Along with time, research of a fuzzy set are combined with algebra that produce fuzzy algebra. One of the research is a fuzzy subgroup and fuzzy level subset. The other research is an anti fuzzy subgroup that is inspired by a fuzzy subgroup. The purpose of this research is to write further study of anti fuzzy subgroup properties by induction of properties of fuzzy algebra such as fuzzy set, fuzzy subgroup, and anti fuzzy subgroup. The research procedure is to study the basic concept of fuzzy set, fuzzy subgroup, and anti fuzzy subgroup. Using that concept to proof the properties of the anti fuzzy subgroup. The conclusions are in the anti fuzzy subgroup, set with anti fuzzy subgroup is a subgroup of a group that can be applied to complement of and normal anti fuzzy subgroup closely related to anti fuzzy left coset, right coset, and middle coset.

Keywords

Group, Subgroup, Coset, Fuzzy Subgroup, Anti Fuzzy Subgroup

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References

Abdi, M., Sukarna, & Abubakar, R. (2018). Suatu Kajian Tentang Grup Fuzzy. Journal of Mathematics Computations and Statistics, 1(1), 78–84. https://doi.org/https://doi.org/10.35580/jmathcos.v1i1.9181

Abdurrahman, S. (2022). Pengantar Struktur Aljabar : Teori Grup. Kalam Emas.

Barnard, T., & Neill, H. (2017). Discovering Group Theory A Transition to Advanced Mathematics (1st ed.). Taylor & Francis Group, LLC.

Chandrasekaran, S., & Deepica, N. (2019). Relation between Fuzzy Subgroups & Anti- Fuzzy Subgroups. IJIRST –International Journal for Innovative Research in Science & Technology, 5(9), 1–5.

Ford, T. J. (2020). Groups. In Introduction to Abstract Algebra (pp. 1–325). Department of Mathematics, Florida Atlantic University, Boca Raton, FL 33431.

Gayen, S., Jha, S., Singh, M., & Prasad, A. (2021). On anti-fuzzy subgroup. Yugoslav Journal of Operations Research, 31(4), 539–546. https://doi.org/10.2298/YJOR200717043G

Jezewski, M., Czabanski, R., & Leski, J. (2017). Introduction to Fuzzy Sets. In Theory and Applications of Ordered Fuzzy Numbers (pp. 3–22). Springer Nature. https://doi.org/10.1007/978-3-319-59614-3

Onasanya, B. (2016). Review of some anti fuzzy properties of some fuzzy subgroups. Annals of Fuzzy Mathematics and Informatics, 11(6), 899–904. http://www.afmi.or.kr/2016-Vol-11-No-06.htm

Onasanya, B., & Ilori, S. (2014). Some Results in Fuzzy and Anti Fuzzy Group Theory. International Journal Of Mathematical Combinatorics, 1(3), 1–5.

Yasir, A., Abdurrahman, S., & Huda, N. (2016). Fuzzy Anti Subgrup. Epsilon: Jurnal Matematika Murni Dan Terapan, 10(2), 48–54. https://doi.org/https://doi.org/10.20527/epsilon.v10i2.37

DOI: https://doi.org/10.20527/epsilon.v17i1.9135