Abstract
Using the belongs to relation (?) and quasi-coincidence with relation (q) between fuzzy points and fuzzy sets, the concept of (?, β)-fuzzy R-subgroup of a near-ring where ? , β are any two of {?, q, ??q , ??q} with ? ? ??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.
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