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FUZZY SUBGROUPS BASED ON FUZZY POINTS

  • Jun, Young-Bae (Department of Mathematics Education (and RINS) Gyeongsang National University) ;
  • Kang, Min-Su (Department of Mathematics Hanyang University) ;
  • Park, Chul-Hwan (School of Digital, Mechanics Ulsan College)
  • Received : 2010.02.01
  • Published : 2011.07.31

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) (${\in}$, ${\in}{\vee}q_{\kappa}$)-fuzzy subgroup;(${\in}$, ${\in}{\vee}q_{\kappa}$)-fuzzy subgroup generated by a fuzzy subset;(${\in}$, ${\in}{\vee}q_{\kappa}$)-fuzzy normal subgroup;(${\in}$, ${\in}{\vee}q_{\kappa}$)-fuzzy left (resp. right) coset;(${\in}$, ${\in}{\vee}q_{\kappa}$)-level subgroup

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