L-fuzzy upper approximation operators associated with L-generalized fuzzy remote neighborhood systems of L-fuzzy points

It is well known that the approximation operators are always primitive concepts in kinds of general rough set theories. In this paper, considering L to be a completely distributive lattice, we introduce a notion of L-fuzzy upper approximation operator based on L-generalized fuzzy remote neighborhood systems of L-fuzzy points. It is shown that the new approximation operator is a fuzzification of the upper approximation operator in the rough set theory based on general remote neighborhood systems of classical points. Then the basic properties, axiomatic characterizations and the reduction theory on the L-fuzzy upper approximation operator are presented. Furthermore, the L-fuzzy upper approximation operators corresponding to the serial, reflexive, unary and transitive L-generalized fuzzy remote neighborhood systems, are discussed and characterized respectively.