- Current Issue - Ahead of Print Articles - All Issues - Search - Open Access - Information for Authors - Downloads - Guideline - Regulations ㆍPaper Submission ㆍPaper Reviewing ㆍPublication and Distribution - Code of Ethics - For Authors ㆍOnline Submission ㆍMy Manuscript - For Reviewers - For Editors
 Fuzzy subgroups based on fuzzy points Commun. Korean Math. Soc. 2011 Vol. 26, No. 3, 349-371 https://doi.org/10.4134/CKMS.2011.26.3.349Published 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 Full-Text :