New results on single axioms for L-fuzzy rough approximation operators

This paper further studies axiomatic characterizations of L-fuzzy rough sets, where L denotes a residuated lattice. Single axioms for upper L-fuzzy rough approximation operators are investigated in two different approaches, which describe upper L-fuzzy approximation operators with ordinary L-fuzzy operations and L-fuzzy product operation, respectively. We characterize upper L-fuzzy rough approximation operators by only one axiom with ordinary L-fuzzy operations, when the L-fuzzy relation is Euclidean as well as the composition of Euclidean with serial (resp. reflexive). We also discuss the single axioms for upper L-fuzzy rough approximation operators with L-fuzzy product operation on arbitrary L-fuzzy relations that are not limited as either general L-fuzzy relations or symmetric L-fuzzy relations. The single axioms for lower L-fuzzy rough approximation operators are discussed with ordinary L-fuzzy operations regardless of the regularity of residuated lattice L. (C) 2019 Elsevier B.V. All rights reserved.