Fuzziness in partial approximation framework

In partial approximation spaces with Pawlakian approximation pairs, three partial membership functions are generated. These fuzzy functions rely on the lower and upper approximations of a set. They provide special type of fuzziness on the universe: all of them are partial functions and derived from the observed data relatively to available knowledge about the objects of the universe.With the help of these functions, three new approximation pairs are generated and so new approximation spaces appear effectively. Using not Pawlakian approximation pairs gives a special insight into the nature of general set approximations, and so new models of necessity and possibility can be given.