Hierarchical relationships of optimal scale combinations in inconsistent generalized multi-scale decision systems
A multi-scale information system is an attribute-value system in which each object under each attribute is represented by different scales at different levels of granulations having a granular information transformation from a finer to a coarser labelled value.For a given multi-scale decision system,a key step is the selection of an optimal scale for each attribute to determine a proper decision table with some requirement for final decision or classification,and such a process is called the optimal scale combination selection.Aiming at the problem of optimal scale combination selection in inconsistent generalized multi-scale decision systems,by introducing tri-level thinking,concepts of optimal scale combinations for generalized decision classes and object scale combinations in inconsistent generalized multi-scale decision systems are first introduced,and the hierarchical relationship between them is discussed.Notions of optimal scale combinations and key scale combinations induced by an attribute reduct are then defined,and the hierarchical relationship between object key scale combinations and generalized decision class key scale combinations is examined.Finally,methods of mutual calculation between key scale combinations of objects and key scale combinations of generalized decision classes are presented.
granular computingrough setsinformation systemmuti-scale information systemoptimal scale combination
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