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Characteristic and Frattini fuzzy submultigroups of fuzzy multigroups

P. A. Ejegwa|J. M. Agbetayo|J. A. Otuwe
기초자연과학연구소 (The Natural Science Institute Wonkwang University)|2020.04|ANNALS OF FUZZY MATHEMATICS AND INFORMATICS|제19권 제2호|pp. 139-155|DOI 10.30948/afmi.2020.19.2.139

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참고문헌

키워드

Fuzzy multisetFuzzy multigroupFuzzy submultigroupNormal fuzzy submultigroupCharacteristic fuzzy submultigroupFrattini fuzzy submultigroup

초록

This paper proposes the notions of characteristic and Frattini fuzzy submultigroups of fuzzy multigroups. Some properties of characteristic fuzzy submultigroups of fuzzy multigroups are outlined and some related results are obtained. It is shown that a fuzzy submultigroup is characteristic if and only if its alpha-cut is a characteristic subgroup, and every characteristic fuzzy submultigroup is a normal fuzzy submultigroup. Also, we put forward the ideas of maximal fuzzy submultigroups and Frattini fuzzy submultigroups of fuzzy multigroups as extensions of maximal subgroups and Frattini subgroups of classical groups. It is presented that every Frattini fuzzy submultigroup is both characteristic and normal, respectively. Finally, some results are established in connection to level subgroups and alpha-cuts of fuzzy multigroups.

Abstract

This paper proposes the notions of characteristic and Frattini fuzzy submultigroups of fuzzy multigroups. Some properties of characteristic fuzzy submultigroups of fuzzy multigroups are outlined and some related results are obtained. It is shown that a fuzzy submultigroup is characteristic if and only if its alpha-cut is a characteristic subgroup, and every characteristic fuzzy submultigroup is a normal fuzzy submultigroup. Also, we put forward the ideas of maximal fuzzy submultigroups and Frattini fuzzy submultigroups of fuzzy multigroups as extensions of maximal subgroups and Frattini subgroups of classical groups. It is presented that every Frattini fuzzy submultigroup is both characteristic and normal, respectively. Finally, some results are established in connection to level subgroups and alpha-cuts of fuzzy multigroups.

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