Fuzzy subgroups based on fuzzy points
Commun. Korean Math. Soc. 2011 Vol. 26, No. 3, 349-371
https://doi.org/10.4134/CKMS.2011.26.3.349
Published online September 1, 2011
Young Bae Jun, Min Su Kang, and Chul Hwan Park
Gyeongsang National University, Hanyang University, Ulsan College
Abstract : Using the ``belongs to'' relation and ``quasi-coincident with'' relation between a fuzzy point and a fuzzy subgroup, Bhakat and Das, in 1992 and 1996, initiated general types of fuzzy subgroups which are a generalization of Rosenfeld's fuzzy subgroups. In this paper, more general notions of ``belongs to'' and ``quasi-coincident with'' relation between a fuzzy point and a fuzzy set are provided, and more general formulations of general types of fuzzy (normal) subgroups by Bhakat and Das are discussed. Furthermore, general type of coset is introduced, and related fundamental properties are investigated.
Keywords : $(\in, \in)$-fuzzy subgroup, (strong) $(\in,$ $\in\! \vee \, {\rm q}_k)$-fuzzy subgroup, $(\in,$ $\in\! \vee \, {\rm q}_k)$-fuzzy subgroup generated by a fuzzy subset, $(\in,$ $\in\! \vee \, {\rm q}_k)$-fuzzy normal subgroup, $(\in, \in\! \vee \,{\rm q}_k)$-fuzzy left (resp. right) coset, $(\in\! \vee \,{\rm q}_k)$-level subgroup
MSC numbers : 20N25, 08A72
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