Abstract: Relation between tolerance class and indispensable attribute and knowledge dependency in rough set model with tolerance relation is explored. After giving definitions and concepts of knowledge dependency and knowledge dependency degree for incomplete information system in tolerance rough set model by distinguishing decision attribute containing missing attribute value or not, the result of maintaining reflectivity, transitivity, augmentation, decomposition law and merge law for complete knowledge dependency is proved. Knowledge dependency degrees (not complete knowledge dependency degrees) only satisfy some laws after transitivity, augmentation and decomposition operations. An algorithm to solve attribute reduction in an incomplete decision table is designed. The correctness is checked by an example.
Abstract: Using maximal consistent blocks of tolerance relation
on the universe in incomplete decision table, the concepts of join block
and meet block are introduced and studied. Including tolerance class,
other blocks such as tolerant kernel and compatible kernel of an object
are also discussed at the same time. Upper and lower approximations
based on those blocks are also defined. Default definite decision rules
acquired from incomplete decision table are proposed in the paper. An
incremental algorithm to update default definite decision rules is
suggested for effective mining tasks from incomplete decision table
into which data is appended. Through an example, we demonstrate
how default definite decision rules based on maximal consistent
blocks, join blocks and meet blocks are acquired and how optimization
is done in support of discernibility matrix and discernibility function
in the incomplete decision table.