Pseudo-quotient space theory for granular computing of non-partition model

Quotient space theory, a general theoretical model of granular computing, is generalized from the viewpoint of granulation. Reflexive and symmetric binary relation, namely compatibility relation, plays the role of granulation. By the construction of homeomorphism, it is proved that most of conclusions of classical quotient space theory keep being valid. The consequent model is called pseudo-quotient space theory. To some degree, the generalization enriches contents of quotient space theory and makes it possible to solve problems of non-partition model.