Characterizations of regular ordered semigroups in terms of (α,β)-fuzzy generalized bi-ideals

  • Authors:
  • Bijan Davvaz;Asghar Khan

  • Affiliations:
  • Department of Mathematics, Yazd University, Yazd, Iran;Department of Mathematics, COMSATS Institute of Information Technology, Abbottabad, Pakistan

  • Venue:
  • Information Sciences: an International Journal
  • Year:
  • 2011

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Abstract

In this paper, the concept of an (@a,@b)-fuzzy generalized bi-ideal in an ordered semigroup is introduced, which is a generalization of the concept of a fuzzy generalized bi-ideal in an ordered semigroup. Using this concept, some characterization theorems are provided. The upper/lower parts of an (@?,@?@?q)-fuzzy generalized bi-ideal are introduced and some characterizations of regular ordered semigroups are given. Also, we consider the concept of implication-based fuzzy generalized bi-ideals in an ordered semigroup. In particular, the implication operators in Lukasiewicz system of continuous-valued logic are discussed.