Translated Title

Translated Abstract

The　classical　rough　set　theory　was　proposed　by　Z.　Pawlak　in　1982　to　deal　with　the　inconsistency　in　datasets.　The　need　of　complex　data　analysis　in　practice　has　led　to　a　variety　of　extensions　of　the　classical　rough　set　model　and　the　extended　rough　sets　have　been　widely　applied　to　many　fields　such　as　data　mining　and　machine　learning.

Both　attribute　reduction　and　rule　acquisition　are　most　important　issues　in　the　applications　of　rough　sets.　In　consideration　of　the　fact　that　a　real-world　dataset　usually　contains　redundant　attributes,　which　can　lead　to　the　consequence　that　the　extracted　rules　are　not　compact,　this　dissertation　focuses　on　the　study　of　attribute　reduction　methods　for　covering　decision　systems,　interval-valued　decision　systems　and　fuzzy　decision　systems　from　the　viewpoint　of　acquiring　compact　rules.　The　main　innovative　work　includes　the　following　aspects:
　
(1)　The　definition　of　decision　rules　and　the　index　of　rule　confidence　in　classical　decision　systems　are　extended　to　the　case　of　covering　decision　systems.　A　concept　of　covering　granular　rules　is　presented,　and　the　implication　relationship　between　the　covering　granular　rules　is　investigated.　Then,　a　confidence　preserved　attribute　reduction　framework　for　covering　decision　systems　is　formulated　to　extract　the　compact　decision　rules　whose　confidence　are　not　less　than　a　pre-specified　threshold.　Furthermore,　a　combinatorial　optimization　algorithm　is　developed　to　compute　all　the　reducts　of　a　covering　decision　system.　Some　numerical　experiments　are　conducted　to　demonstrate　the　validity　of　the　proposed　reduction　method.

(2)　By　defining　a　proper　binary　relation　on　an　interval-valued　information　system,　the　concept　of　an　interval-valued　granular　rule　is　proposed　and　a　new　index　is　introduced　to　measure　the　confidence　of　an　interval-valued　granular　rule.　Then,　the　issue　of　extraction　both　compact　certain　rules　and　some　compact　possible　rules　with　certain　confidence　levels　is　studied,　and　a　confidence　preserved　attribute　reduction　framework　is　established　for　interval-valued　decision　systems.　A　combinatorial　optimization　approach　is　suggested　to　compute　all　the　reducts　of　an　interval-valued　decision　system.　Furthermore,　some　numerical　experiments　are　conducted　to　evaluate　the　performance　of　the　reduction　approach　and　the　gain　of　using　the　possible　rules　in　making　decision.

(3)　The　granular　structures　of　fuzzy　rough　sets　are　established　based　on　generic　fuzzy　relations.　With　the　granular　structures　of　the　lower　approximations,　the　concept　of　fuzzy　granular　rules　is　presented　for　fuzzy　decision　systems.　An　attribute　reduction　framework　for　fuzzy　decision　systems　is　formulated　to　extract　compact　fuzzy　granular　rules.　Furthermore,　a　Boolean　reasoning　method　is　proposed　to　compute　all　the　reducts,　and　a　heuristic　algorithm　is　also　provided　to　search　for　one　of　the　reducts.　A　classifier　is　finally　constructed　to　demonstrate　the　application　of　the　fuzzy　granular　rules,　and　some　numerical　experiments　are　conducted　to　assess　the　performance　of　the　classifier.

(4)　Based　on　the　granular　structure　of　the　fuzzy　lower　approximation,　a　novel　information　entropy　is　presented　for　mixed　data.　The　entropy　is　used　to　equivalently　characterize　the　attribute　reduction　of　fuzzy　rough　sets.　Furthermore,　a　feature　selection　algorithm　based　on　the　entropy　is　developed　for　mixed　data,　and　some　numerical　experiments　are　conducted　to　demonstrate　the　efficiency　of　the　improved　algorithm.

Translated Keyword

[Attribute reduction, Decision systems, Feature selection, Rough sets, Rule acquisition]

Research Interests

Classification

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