Fuzzy R-subgroups with thresholds of near-rings and implication operators

  • Authors:

  • B. Davvaz

  • Affiliations:

  • Yazd University, Department of Mathematics, Yazd, Iran

  • Venue:
  • Soft Computing - A Fusion of Foundations, Methodologies and Applications
  • Year:
  • 2008

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Abstract

Using the belongs to relation (∈) and quasi-coincidence with relation (q) between fuzzy points and fuzzy sets, the concept of (α, β)-fuzzy R-subgroup of a near-ring where α , β are any two of {∈, q, ∈∨q , ∈∧q} with α ≠ ∈∧q is introduced and related properties are investigated. We also introduce the notion of a fuzzy R-subgroup with thresholds which is a generalization of an ordinary fuzzy R-subgroup and an (∈, ∈∨q)-fuzzy R-subgroup. Finally, we give the definition of an implication-based fuzzy R-subgroup.