  We study properties of classes of closure operators and closure systems
parameterized by systems of isotone Galois connections. The parameterizations
express stronger requirements on idempotency and monotony conditions of closure
operators. The present approach extends previous approaches to fuzzy closure
operators which appeared in analysis of object-attribute data with graded
attributes and reasoning with if-then rules in graded setting and is also
related to analogous results developed in linear temporal logic. In the paper,
we present foundations of the operators and include examples of general
problems in data analysis where such operators appear.
