The rough representation and measurement of quotient structure in algebraic quotient space model

Granular computing is a very hot research field in recent years.In our previous work an alge-braic quotient space model was proposed, where the quotient structure could not be deduced if the granulation was based on an equivalence relation.In this paper, definitions were given and formulas of the lower quotient congruence and upper quotient congruence were calculated to roughly represent the quotient structure.Then the accuracy and roughness were defined to measure the quotient struc-ture in quantification.Finally, a numerical example was given to demonstrate that the rough repre-sentation and measuring methods are efficient and applicable.The work has greatly enriched the al-gebraic quotient space model and granular computing theory.