Inconsistent Degree And Evidence-theory-based Algorithms Of Attribute Reduction In Inconsistent Decision Tables

Information system is a database which contains the relationship of objects andattributes(condition attributes and decision attributes). The definition of inconsistentdecision rule pairs is proposed in an inconsistent decision table. Inclusion degree is usedto select the equivalence classes which can produce inconsistent decision rule pairs, thendiscernibility matrix is employed to extract inconsistent decision rule pairs, thus thenumber of inconsistent decision rule pairs can be calculated in inconsistent decision table.The number can be also calculated by the component of generalized decision functiondirectly. And then the inconsistent degree of an inconsistent decision table is computed.Finally, the relationship of inconsistent degree between original inconsistent decision tableand the reduced inconsistent decision table is compared.Evidence theory uses the mass function(probability distribution function), belieffunction and plausibility function to deal with uncertainty problem. The classical roughset theory and evidence theory have a close relationship in which dual nonnumerical upperand lower approximation operators can be understood as the corresponding numerical ofduality belief function and plausibility function. A numerical characteristics of the at-tribute reduction algorithm based on evidence theory is proposed. By using this method,the change of inconsistent degree of an inconsistent decision table is analyzed.Multigranulation rough set is generalized from a classical rough set with a singleindiscernibility binary relation extending to multiple indiscernibility binary relation. At-tribute reduction in classical rough set could be described by belief function and the plau-sibility function, thus it has proved that attribute reduction in multigranulation roughset can also be described by attribute reduction based on evidence theory. On this basis,evidence-theory-based algorithms of attribute reduction are obtained in multigranulationrough set. Finally, the inconsistent degree of multigranulation inconsistent decision tableis studied.