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GENERAL TYPES OF (α,β)-FUZZY IDEALS OF HEMIRINGS

  • Jun, Y.B. (Department of Mathematics Education, Gyeongsang National University) ;
  • Dudek, W.A. (Institute of Mathematics and Computer Science, Wroclaw University of Technology Wyb.) ;
  • Shabir, M. (Department of Mathematics, Quaid-i-Azam University) ;
  • Kang, Min-Su (Department of Mathematics, Hanyang University)
  • Received : 2010.07.26
  • Accepted : 2010.08.26
  • Published : 2010.09.25

Abstract

W. A. Dudek, M. Shabir and M. Irfan Ali discussed the properties of (${\alpha},{\beta}$)-fuzzy ideals of hemirings in [9]. In this paper, we discuss the generalization of their results on (${\alpha},{\beta}$)-fuzzy ideals of hemirings. As a generalization of the notions of $({\alpha},\;\in{\vee}q)$-fuzzy left (right) ideals, $({\alpha},\;\in{\vee}q)$-fuzzy h-ideals and $({\alpha},\;\in{\vee}q)$-fuzzy k-ideals, the concepts of $({\alpha},\;\in{\vee}q_m)$-fuzzy left (right) ideals, $({\alpha},\;\in{\vee}q_m)$-fuzzy h-ideals and $({\alpha},\;\in{\vee}q_m)$-fuzzy k-ideals are defined, and their characterizations are considered. Using a left (right) ideal (resp. h-ideal, k-ideal), we construct an $({\alpha},\;\in{\vee}q_m)$-fuzzy left (right) ideal (resp. $({\alpha},\;\in{\vee}q_m)$-fuzzy h-ideal, $({\alpha},\;\in{\vee}q_m)$-fuzzy k-ideal). The implication-based fuzzy h-ideals (k-ideals) of a hemiring are considered.

Keywords

$({\alpha},\\in{\vee}q_m)$-fuzzy left (right) ideal;$({\alpha},\\in{\vee}q_m)$-fuzzy h (k)-ideal;fuzzifying left (right) ideal;fuzzifying h (k)-ideal;t-implication-based fuzzy left (right) ideal;t-implication-based fuzzy h (k)-ideal

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  2. Ordered semigroups characterized by ( $${ \in,\in \vee q}_{k}$$ )-fuzzy generalized bi-ideals vol.21, pp.S1, 2012, https://doi.org/10.1007/s00521-011-0731-2
  3. Characterizations of hemirings by (,qk)-fuzzy ideals vol.61, pp.4, 2011, https://doi.org/10.1016/j.camwa.2010.12.056