Generalized fuzzy h-bi-ideals and h-quasi-ideals of hemirings

  • Authors:

  • Xueling Ma;Jianming Zhan

  • Affiliations:

  • Department of Mathematics, Hubei Institute for Nationalities, Enshi, Hubei Province 445000, PR China;Department of Mathematics, Hubei Institute for Nationalities, Enshi, Hubei Province 445000, PR China

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2009

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Abstract

A new kind of generalized fuzzy h-ideals of a hemiring, namely, the (set membership, variant,set membership, variantlogical orq)-fuzzy h-bi-ideal (resp., h-quasi-ideal) is studied and the relationships between these generalized fuzzy h-ideals are described. Some characterization theorems of prime and semiprime (set membership, variant,set membership, variantlogical orq)-fuzzy h-bi-ideals (resp., h-quasi-ideals) of a hemiring are also given. In particular, we show that the h-hemiregular hemirings and h-intra-hemiregular hemirings can be described by using some of their generalized fuzzy h-ideals. Finally, the implication-based fuzzy h-bi-ideals (resp., h-quasi-ideals) of a hemiring are considered.