Commun. Korean Math. Soc. 2011; 26(3): 349-371
Printed September 1, 2011
https://doi.org/10.4134/CKMS.2011.26.3.349
Copyright © The Korean Mathematical Society.
Young Bae Jun, Min Su Kang, and Chul Hwan Park
Gyeongsang National University, Hanyang University, Ulsan College
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
MSC numbers: 20N25, 08A72
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