Study For Granular Computing Model Based On Quotient Space Theory

The quotient space theory(QST) is currently one of mainstream granular computing models.The domain structure in the existing quotient space model(QSM) is usually a topology.However,two basic conclusions of the existing QSM are still valid or not if the domain structure is an al-gebraic structure.As a starting point,this thesis deeply studies QSM with an algebraic structure,and comparatively analyses with the existing QSM in terms of composition and decomposition.The thesis introduces the concept of congruence relation,and systematacially demonstrates the completeness and characteristics pre-serving.That’s to say,the whole of congruence relations forms a complete semi-order lattice,and the false-preserving principle and true-preserving principle still valid in QSM with an algebraic structure.It defines the concepts of least upper (great lower) congruence corresponding to least upper (great lower) quotient,concisely proves their existence from the equivalent relation,and acquires some important related conclusions.It proposes a multi-granular computing architecture,i.e., a top-down decomposition and bottom-up synthesis.The structure plays a very im-portant role in QST,and the QSMs with different structures are different.A composition of topologies of different quotient spaces is generally not a quotient topology,while a composition of operators of different quotient spaces is a quotient operator.As for decomposition, it acquires the two important conclusions when defining the concepts of problem equiva-lence and reversible decomposition.One is that chained granulation is equivalent to directed granulation,and the other is that an orthogonal de-composition in QSM with an algebraic structure is reversible,but a similar conclusions is not true in QSM with a topological structure.Algebraic is also a common and very important domain struc-ture,therefore the thesis extends the existing QSM in structure, and pro-vides good basis for the combination of quotient space theory and alge-braic theory.