Mathematical formalization of attribute partial order formal structure
Attribute partial order formal structure,as a new theory of knowledge discovery and knowledge representation based on human cognitive principles and granular computing ideas,has been widely used at present.However,its theoretical basis is lack of abstraction and mathematization,which is bound to affect the systematic development of this theory.Regarding the above problem,the mathematical formal description of attribute partial order formal structure is studied.Firstly,a formal framework of knowledge representation is proposed based on the idea of granular computing.On this basis,by defining the cover and the simplest cover of an object set,the concepts of granule and granular group of attribute partial order formal structure are given.And then through the discussion of the sufficient and necessary condition for a granule to derive a granular group,the knowledge structure in attribute partial order formal structure is given,so as to complete the mathematical formal description of attribute partial order formal structure.Finally,through specific examples,the process of constructing attribute partial order formal structure by using mathematical formal description is demonstrated,and the human cognitive law embodied in this process is revealed as well.
formal contextmathematical formalizationattribute partial order formal structuregranular computingconcept cognitive learning
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