Variable precision multigranulation rough fuzzy set approach to multiple attribute group decision-making based on λ-similarity relation

•A λ-similarity relation over multiple fuzzy decision-making information systems.•A λ-similarity relation-based variable precision multigranulation rough set model.•A λ-similarity relation-based variable precision multigranulation rough fuzzy set model.•A method of MAGDM with established variable precision multigranulation rough fuzzy set.