A rough set model based on (L, M)-fuzzy generalized neighborhood systems: a constructive approach

Considering L and M being different commutative quantales, this paper mainly proposes a many-level version of L-fuzzy generalized neighborhood systems and then a pair of many level upper and lower rough approximation operators based on it are defined and discussed. It is proved that these approximation operators include L-fuzzy generalized neighborhood-based approximation operators and M-level L-fuzzy relation-based approximation operators as their special circumstances. Moreover, we define the measure of many level rough approximations that in a certain sense characterizes the quality of the obtained approximation. Furthermore, when the M-level L-fuzzy generalized neighborhood system is non-increasing, serial, reflexive, transitive, and unary, then the corresponding M-level L-rough approximation operators are discussed and characterized, respectively. Moreover, the relationship between M-level L-rough approximation operators and (L,M)-quasi-fuzzy topologies is presented.