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Journal : M A T H L I N E : Jurnal Matematika dan Pendidikan Matematika

CHARACTERIZATION OF NORMAL FUZZY SUBGROUP Cahyo, Bagas Dwi; Suroto, Suroto; Maryani, Sri
Mathline : Jurnal Matematika dan Pendidikan Matematika Vol. 10 No. 2 (2025): Mathline : Jurnal Matematika dan Pendidikan Matematika
Publisher : Universitas Wiralodra

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.31943/mathline.v10i2.791

Abstract

In this article, we discuss the characterization of a normal fuzzy subgroup of classical group . The discussion of this characterization is carried out using Abelian properties, fuzzy conjugate subgroups, fuzzy normalizers, ????-level sets, and fuzzy cosets. The result shows that a sufficient and necessary condition for a normal fuzzy subgroup is the fulfilment of the Abelian condition in the fuzzy subgroup. Then, the equality between of the membership value of all element of  and its conjugate elements is also a sufficient and necessary condition for normal fuzzy subgroup of ????. Moreover, sufficient and necessary conditions of the normal fuzzy subgroup are the normalizer of this fuzzy subgroup is equal to ????. Henceforth, the sufficient and necessary conditions of a normal fuzzy subgroup of  is its ????-level set is a normal subgroup of . Meanwhile, the similarity of the fuzzy right coset and fuzzy left coset of the fuzzy subgroup is also a sufficient and necessary condition for the normal fuzzy subgroup. Furthermore, the normal properties of subgroups on classical groups are a special case of the normal properties in fuzzy subgroups.
Co-Authors - Ardiansyah, - -, Lolytasari Ali, Waleed Amil, Amil Arfah, Arfah Ari Wardayani, Ari Ariadhy, Suseno Arrahman, Rudi Artawan Gede Astriani, Aveny Septi Bukman Lian, Bukman Cahyo, Bagas Dwi Dewi Rosanti, Dewi Diah Setyorini Gunawan Dian Mutiara, Dian Dwi Anggraeni Dwi Rohman Soleh, Dwi Rohman Ekowati Retnaningsih Ertinawati, Yuni Erwin Erwin Fertilita, Soilia Guswanto, Bambang Hendriya Hakim, Fikri Halim, Nurfadhlina Abdul Hamdi Hamdi Hendi Efendi, Hendi Husnul, Nisatami Ichsan Fauzi Rachman Icuk Rangga Bawono, Icuk Rangga Idha Sihwaningrum Jajang Jajang Jamilah, Ai Siti Nur Juwita, Diana karenina, Tili Kharisa, Aflakha Kulsum, Dewi Ummu Kusumasari, Wardany Larasti, Veny Limbar Jaya, Futu Widiana Mariani, Dini Martha Nengah Mufreni, Sadr Lufti Mugi Lestari, Mugi Mulki Indana Zulfa, Mulki Indana Neni Marlina Novriadhy, Dian Nunung Nurhayati Nunung Nurjanah Nurjamilah, Ai Siti Nurmiwati, Nurmiwati Nuryanto Nuryanto Oom Komalasari Pardomuan Robinson Sihombing Parji Parji Patimah, Siti Papat Pitrianti, Siti Primasari, Dwi Ammelia Galuh Purwantho, Herry Puspita, Shafa Nanda Qonitah Faizatul Fitriyah Rahman, Ichsan Fauzi Reni Oktarina Rifda Naufalin Rizqi, Safina Sabila ROHANA ROHANA Rusdi Machrizal Sardjono, Herning Suryo Sheilliarika, Wella Ayu Suhada, Dede Bagus Sulasih Sulasih Suparmanto Supriyanto Supriyanto Suroto Suroto Suwardi Suwardi Suyasa, Made Thursina, Mulyani Titin Setiartin, Titin Triyanna Widiyaningtyas Weni Novandari Wijayanto, Danur Wulandari, Ratna Rizky Yasinta, Tia Yayat Suryati Yogaswara, Angga Zaenafi, Zaenafi Zahratunnisa, Siti Fauziah Zahrotul Munawwaroh