SLIDE 3 ✿➫▲ ⑦ ❖◗❶➓▲✧Ô▼➦➧Ý➡❖◗P ➥ P✙❶✌❘ ➚ ❦✓❫✩❨ ❝❞❱❪❭ ❭ ❦➟➅❪❛✏✹✌❬✝❛➹❱❳❲✮❲✶❴✟❨ ♦❪❧②❲◗❛❤❡▼❡❤❧✝❝✝❻➀❲✸❻✝❱❳❲▼è➙❨ ❡✙③✎❩✢❬❳❩✩❲✮❩✔❬✩❨ ❝ ❨ ❬➟❛❞❱✝❝✝❻ ❐ ❲✸❴✟❨ ❝❤❲❹➅✩❩✢③➄❨ ❬✝❱❪❬✝❝❞❛ ➣✑❝✝❻❳❩✔❨ ❝❞❛➀➁➙❡❣❲✸❴❋❨ ❝❤❲✸❭ ❦♠➅✩❩✢③➄❨ ❬❳❱❳❲◗❛❤❡✙❝✝❻❳❩✔❨ ❝❞❛➹❾➙❨ ➞
❋ ï ➏✉➁➀➒①❰✱❋ ï ➏✟❾➄➒ ❽♥❱❪❬✝➅➘❻✝❛✝❬✝❝❞❛➟è➀➏✉➁➀➒➧❰✧è➀➏✟❾➄➒◗➃
1
X
2
X A B C D
1
X
2
X A B C This region dominates A
Deterministic attributes Uncertain attributes
❐ ❲✸❴✟❨ ❝❤❲❹➅✩❩✢③➄❨ ❬✝❱❪❬✝❝❞❛➹❡✶❛✝❭ ➅✩❩✢③à❻❳❩✢❭ ➅✩❡➄❨ ❬♣❫❵❴ ❱✝❝❞❲❣❨ ❝❞❛ ✪✬✫ ✭✮✪✝✯ ✰ ✱ ✲ ✳ ✴✶✵ ✷✸✯ ✹ ✺ ✻ ✼ ✹ ✽✬✺ ✴ ✴ ✳ ✰ ✰ ✻ ✾ ✲✮✿ ✳ ✹ ✳ ✼ ❀✬❁ ✼ ❂ ✱ ❃ ❄ ❅ ❆ ❆ ❇ ❈ ❉ ✻ ❊ ✹ ✳ ✼✬❅
➢ ✿➫▲✢➦✎❶✂✁ ➥ ❷✓▲☎❖◗❶➠Ô✙➦➫Ý➡❖❣P ➥ P✙❶✌❘
0.2 0.4 0.6 0.8 1 1.2
- 6
- 5.5
- 5
- 4.5
- 4
- 3.5
- 3
- 2.5
- 2
Probability Negative cost S1 S2 0.2 0.4 0.6 0.8 1
- 6
- 5.5
- 5
- 4.5
- 4
- 3.5
- 3
- 2.5
- 2
Probability Negative cost S1 S2
qØ❨ ❡◗❲✸❴✟❨ ♦❪❧❳❲✶❨ ❩✢❬➹➌☎êØ❡❣❲♥❩✔❝✝❻✝❱❳❡❣❲❣❨ ❝❞❱❪❭ ❭ ❦♣➅✩❩✢③➄❨ ❬✝❱❳❲◗❛❤❡ ➅✔❨ ❡◗❲✸❴✟❨ ♦✩❧❳❲✶❨ ❩✢❬❥➌❈✭❹❨ ➞
✞✠✟ ➌➓ê✸➏✦✥✖➒☛✡✮✥✌☞✍✄✝✆ ✞✠✟ ➌❈✭❞➏■▼◗➒✎✡◆▼ ➩ ❜➫è➙❨ ❡➄③✎❩✢❬❳❩❵❲✮❩✢❬✩❨ ❝➟❨ ❬✯✥☛❿✔❲✸❻✝❛✝❬➀❾❥ê⑩s✎❨ ❲✶❻➀❩✢❧❳❲✮❝❞❩✢③▼❛❥➅✓❨ ❡❣❲✶❴✟❨ ♦❪❧②❲✶❨ ❩✔❬❥➌➓ê ❡◗❲✮❩✔❝✝❻✝❱❳❡◗❲✶❨ ❝❞❱❪❭ ❭ ❦♣➅❵❩✢③➄❨ ❬✝❱❳❲◗❛❤❡✙❾ ✭Øs✎❨ ❲✸❻➀❩✔❧❳❲◗❝❤❩✢③▼❛❥➅✔❨ ❡◗❲✸❴✟❨ ♦❪❧❳❲✶❨ ❩✢❬➄➌❈✭❞➣ ✄ ✟ ✞✠✟ ➌➓ê✸➏✩✥✌➒✶è➀➏✦✥✖➒☛✡✮✥Ò❰✏✄ ✟ ✞✠✟ ➌❈✭❞➏✩✥✌➒✶è➀➏✦✥✖➒☛✡✮✥ ✐♠❧❪❭ ❲✶❨ ❱❳❲♥❲✸❴✟❨ ♦✩❧✝❲◗❛✎❝❞❱❳❡✶❛✩➣✡❡❣❲♥❩✔❝✝❻✝❱❳❡❣❲❣❨ ❝✎➅✩❩✢③➄❨ ❬❳❱❪❬✝❝❞❛✎❩✢❬▼❱❪❭ ❭❵❱❳❲✮❲✸❴❋❨ ♦❪❧❳❲✮❛❞❡➠➭ ❩✢❫②❲✶❨ ③▼❱❪❭ ✪✬✫ ✭✮✪✝✯ ✰ ✱ ✲ ✳ ✴✶✵ ✷✸✯ ✹ ✺ ✻ ✼ ✹ ✽✬✺ ✴ ✴ ✳ ✰ ✰ ✻ ✾ ✲✮✿ ✳ ✹ ✳ ✼ ❀✬❁ ✼ ❂ ✱ ❃ ❄ ❅ ❆ ❆ ❇ ❈ ❉ ✻ ❊ ✹ ✳ ✼✬❅
Ó ✿➫▲✢➦✎❶✑✁ ➥ ❷❪▲☎❖◗❶➷Ô▼➦➫Ý➡❖❣P ➥ P✙❶✌❘➙❶✌➦➧P➫▲✥Ô➀Õ ❐ ❲✮❩✔❝✝❻✝❱❳❡◗❲✶❨ ❝➹➅✩❩✢③➄❨ ❬✝❱❪❬❳❝②❛➹❝②❱❪❬➹❩❵❜❋❲◗❛✝❬➛♦✩❛❥➅✩❛❞❲✮❛❵❴✉③➄❨ ❬✝❛❞➅➛s❹❨ ❲✸❻②❩✢❧❳❲ ❛✸➳❵❱✝❝❤❲➧➅✔❨ ❡❣❲✶❴✟❨ ♦❪❧②❲✸❨ ❩✢❬❳❡➹❧②❡❤❨ ❬②❺✺✛✢❧✝❱❪❭ ❨ ❲✮❱❳❲✶❨ ➲❵❛ ❴✬❛❞❱❳❡❣❩✔❬✩❨ ❬❳❺ ð➓➂ ✛☎➂ ❿✢❝❞❩✔❬❳❡❣❲✸❴✟❧✝❝❤❲✶❨ ❩✢❬♠❝❤❩✩❡❣❲❹❨ ❬✝❝✝❴✬❛❞❱❳❡✶❛❤❡✎s✎❨ ❲✶❻➀➅✔❨ ❡❣❲◗❱❪❬❳❝②❛❥❜✮❴ ❩✢③➠❝✝❨ ❲✟❦ ë✌✭❹❨ ❡❹❜✮❧❪❴ ❲✶❻✝❛✝❴⑩❜✮❴ ❩✢③➷❲✸❻❳❛➄❝✝❨ ❲✟❦➀❲✸❻✝❱❪❬♠ë✖ê ➭ ë✖ê✑❡❣❲♥❩✔❝✝❻✝❱❳❡❣❲❣❨ ❝❞❱❪❭ ❭ ❦➛➅✩❩✢③➄❨ ❬✝❱❳❲◗❛❤❡➄ë ✭①❩✢❬➀❝❤❩✩❡◗❲ ð➓➂ ❺☎➂ ❿☎❨ ❬✚✎✶❧❪❴ ❦➛❨ ❬✝❝✝❴✬❛❞❱❳❡✶❛❤❡✎s✎❨ ❲✶❻➀❝❤❩✢❭ ❭ ❨ ❡❤❨ ❩✢❬➟❡❞❫✩❛❞❛❞➅ ➸ ❱❪❬➀❱❪❬❪❬❳❩✩❲✮❱❳❲◗❛➟♦✩❛✝❭ ❨ ❛✸❜✎❬✝❛❤❲✟sØ❩✓❴✉t❞❡➫s✎❨ ❲✶❻➹❡❣❲♥❩✔❝✝❻✝❱❳❡❣❲✶❨ ❝➀➅✩❩✢③➄❨ ❬✝❱❪❬✝❝❞❛♠❨ ❬❞❜❋❩✓❴✉③▼❱❳❲✶❨ ❩✢❬✓➣ ❋✓✒ ➑✕✔✗✖ ❽✸❋➬❫❵❩✩❡✸❨ ❲✶❨ ➲❵❛❵❭ ❦r❨ ❬✙✘✌❧✝❛✝❬✝❝❞❛❤❡ ✖ ➃✎③▼❛❞❱❪❬❳❡❹❲✸❻✝❱❳❲ × ❩✓❴✡❛❤➲❵❛✝❴ ❦➹➲❵❱❪❭ ❧✝❛✛✚➟❩❵❜ ✖✢✜ ❡❹❩❵❲✸❻✝❛✝❴①❫✝❱❵❴✬❛✝❬❳❲✮❡✤✣
✥✖êØ❰✬✥✌✭Ø➭✦✥➟➏ ✖★✧ ✥✖ê✶➍✩✚✔➒☎❡◗❲✮❩✔❝✝❻✝❱❳❡◗❲✶❨ ❝❞❱❪❭ ❭ ❦▼➅❵❩✢③➄❨ ❬✝❱❳❲✮❛❞❡✪✥➟➏ ✖★✧ ✥✔✭❤➍✩✚✔➒ ✪✬✫ ✭✮✪✝✯ ✰ ✱ ✲ ✳ ✴✶✵ ✷✸✯ ✹ ✺ ✻ ✼ ✹ ✽✬✺ ✴ ✴ ✳ ✰ ✰ ✻ ✾ ✲✮✿ ✳ ✹ ✳ ✼ ❀✬❁ ✼ ❂ ✱ ❃ ❄ ❅ ❆ ❆ ❇ ❈ ❉ ✻ ❊ ✹ ✳ ✼✬❅
Ú ✫ Ü✎➥ Ý ➨➄◆◗❘✭✬⑧❶ ➥Ø⑦ ❖◗P➄❷✔❏ ⑦✥➥ P✙❶✌❘ ✁❑❻❵❨ ❝✝❻♠❱❵❴✬❝❤❡✎❱❵❴✬❛➟❫✝❩✩❡❤❨ ❲✶❨ ➲❵❛➄❩✓❴Ø❬❳❛❞❺✩❱✝❲❣❨ ➲❵❛➟❨ ❬✙✘✌❧✝❛✝❬✝❝❞❛❤❡☎✄
SocioEcon Age GoodStudent ExtraCar Mileage VehicleYear RiskAversion SeniorTrain DrivingSkill MakeModel DrivingHist DrivQuality Antilock Airbag CarValue HomeBase AntiTheft Theft OwnDamage PropertyCost LiabilityCost MedicalCost Cushioning Ruggedness Accident OtherCost OwnCost
✪✬✫ ✭✮✪✝✯ ✰ ✱ ✲ ✳ ✴✶✵ ✷✸✯ ✹ ✺ ✻ ✼ ✹ ✽✬✺ ✴ ✴ ✳ ✰ ✰ ✻ ✾ ✲✮✿ ✳ ✹ ✳ ✼ ❀✬❁ ✼ ❂ ✱ ❃ ❄ ❅ ❆ ❆ ❇ ❈ ❉ ✻ ❊ ✹ ✳ ✼✬❅
❘⑩⑨❤❘ ⑦ ❘☛P✙❶✌❘➙❷✓▲ ⑦ ❏✙❶➓▲✥❏ ⑦ ❘✭✬ ❅ ❘✡▲✔❘ ⑦ Ý➡❖◗P➄❖❣❷❪▲☎❖❣❶ ❋♣ê①❱❪❬✝➅☛❋☛✭▼❫❵❴✬❛✸❜✟❛✝❴✬❛✝❬❳❲✶❨ ❱✓❭ ❭ ❦r❨ ❬✝➅✩❛❵❫❵❛✝❬✝➅✓❛✝❬✝❲ ❩❵❜✓❋✯✮▼❨ ➞ ❫❵❴✬❛✸❜✟❛✝❴✬❛✝❬✝❝❞❛♣♦✩❛❤❲✟s①❛❞❛✝❬✱✰✩✥ ê ➍●✥ ✭ ➍✚✥ ✮✳✲ ❱❪❬✝➅✴✰✩✥ ✣ ê ➍✚✥ ✣ ✭ ➍✚✥ ✮✵✲ ➅✩❩✓❛❞❡➄❬❳❩✩❲➫➅❪❛✝❫✩❛✝❬✝➅r❩✔❬✯✥✂✮ ð➓➂ ❺☎➂ ❿✶✰✸❘❚❙✾❯✚◗✠❏❪➍✸➶✻❙❃◗✠▼✸➍✸ë✓❑✸✷✔❏▲▼☛✹ ✲ ➣ ✰✩❱❃❂✥❿ ❂❃❂❃❂➟❡❞❧❞➞✖❛✝❴✮❿✂✺✝æ☎➂ ✻r♦❵❨ ❭ ❭ ❨ ❩✢❬✓❿✌❂✥➂ ❂✼✻♠➅❪❛❞❱❳❲✸❻❳❡✵✽❪③❥❫❪③ ✲ ➲✝❡❳➂ ✰✿✾❃❂✥❿ ❂❃❂❃❂➟❡❞❧❞➞✖❛✝❴✮❿✂✺✝æ☎➂ ❱r♦❵❨ ❭ ❭ ❨ ❩✢❬✓❿✌❂✥➂ ❂✼✻♠➅❪❛❞❱❳❲✸❻❳❡✵✽❪③❥❫❪③ ✲ ➚ ❻✝❛❤❩✓❴✬❛✝③ ❽ ➆ ❛❤❩✢❬❳❲✶❨ ❛❤❜❣❿rÙ②ã❵æ✠✾✓➃✸➣➙❨ ❜r❛✸➲✩❛✝❴ ❦↕❫✝❱✩❨ ❴♣❩❵❜r❱❳❲♥❲✸❴✟❨ ♦✩❧❳❲◗❛❤❡➾❨ ❡❁❀✢➂ ➩ ➂✎❩❵❜✂❨ ❲✮❡ ❝❤❩✢③❥❫❪❭ ❛✝③▼❛❵❬②❲❞❿✑❲✶❻✝❛✝❬➘❛✸➲❵❛✝❴ ❦✂❡❤❧❪♦❳❡❣❛❞❲➄❩❵❜➧❱❳❲✮❲✸❴✟❨ ♦❪❧❳❲✮❛❞❡➛❨ ❡✢❀✥➂ ➩ ❩❵❜▼❨ ❲♥❡➹❝❞❩✢③❥❫✩❭ ❛✝③▼❛❵❬②❲❞➣ ③❥❧②❲✸❧✝❱❪❭✶❀✥➂ ➩ ➂ ➂ ➚ ❻✝❛❤❩✓❴✬❛✝③ ❽✸q☛❛❵♦❵❴ ❛❵❧✔❿✡Ù❞ã✼✻❃❂✓➃❤➣①③❥❧❳❲✸❧❳❱✓❭✶❀✢➂ ➩ ➂➠➭ ➮➛❱✝➅❪➅✓❨ ❲✶❨ ➲❵❛ ➲❵❱❪❭ ❧✝❛✙❜✮❧❪❬✝❝❤❲✶❨ ❩✢❬✔➣ ✴♠➏♥ë✑➒Ø➈➠î➹ï✦✴✢ï✉➏✩❋➟ï✉➏♥ë✑➒❣➒ ❊ ❛✝❬✝❝❞❛❥❱❳❡❣❡✶❛❤❡◗❡❃❂Ò❡❤❨ ❬❳❺✢❭ ❛❤Ö✮❱❳❲♥❲✸❴✟❨ ♦✩❧✝❲◗❛❥❜✮❧❪❬❳❝❞❲❣❨ ❩✢❬❳❡②å✥❩❵❜❋❲◗❛✝❬➟❱➹❺✩❩❪❩✔➅➛❱❪❫✩❫❵❴ ❩❳➳❪❨ ③▼❱❳❲✶❨ ❩✢❬ ✪✬✫ ✭✮✪✝✯ ✰ ✱ ✲ ✳ ✴✶✵ ✷✸✯ ✹ ✺ ✻ ✼ ✹ ✽✬✺ ✴ ✴ ✳ ✰ ✰ ✻ ✾ ✲✮✿ ✳ ✹ ✳ ✼ ❀✬❁ ✼ ❂ ✱ ❃ ❄ ❅ ❆ ❆ ❇ ❈ ❉ ✻ ❊ ✹ ✳ ✼✬❅
✑ ⑥⑧⑦ ❘⑩⑨✸❘ ⑦ ❘☛P➄❶✌❘➋❷✓▲ ⑦ ❏✙❶➓▲✥❏ ⑦ ❘✭✬✒✿➫▲✢➦✎❶✑✁ ➥ ❷❪▲☎❖◗❶ → ❛❞❛②➅♠❲✮❩♣❝❤❩✢❬❳❡✸❨ ➅❪❛✝❴①❫❵❴✬❛❤❜✟❛✝❴✬❛✝❬✝❝❞❛❤❡▼❩✝➲✩❛✝❴①❭ ❩✩❲✮❲✮❛❵❴✟❨ ❛❤❡❳➣ ❄ ❨ ❡✙❧❳❲✶❨ ❭ ❨ ❲✟❦❳Ö❣❨ ❬❳➅❪❛✝❫❪❛✝❬❵➅❪❛✝❬✝❲ ❩❵❜❆❅ ❨ ➞ ❫❵❴✬❛✸❜✟❛✝❴✬❛✝❬✝❝❞❛❞❡▼❩❵➲❵❛✝❴Ø❭ ❩✩❲✮❲◗❛✝❴✟❨ ❛❞❡ ❄ ➅❵❩➘❬❳❩✩❲➫➅❪❛✝❫✩❛✝❬✝➅➛❩✢❬✛❇ ✐♠❧❳❲✸❧❳❱❪❭✡❢Ø➂ ➩ ➂ ➣✑❛❞❱✝❝✝❻➀❡❤❧❪♦❳❡✶❛❤❲✎❨ ❡➹❢①➂ ➩ ❩✝❜①❨ ❲✮❡✎❝❤❩✢③❥❫❪❭ ❛✝③▼❛✝❬❳❲ ➭ ➮➘③❥❧✩❭ ❲✶❨ ❫❪❭ ❨ ❝❞❱✝❲✶❨ ➲❵❛ ❧②❲✶❨ ❭ ❨ ❲✟❦➹❜◗❧✩❬✝❝❤❲✶❨ ❩✢❬✓➣ è➝➈ ✧✓ê❣èØê✌✪✬✧❃✭✸è✓✭ ✪✬✧✼✮✸è❈✮ ✜ ✧✔ê ✧❃✭✸èØê◗è✓✭✝✪✬✧✮✭●✧✝✮❤è✓✭❣è❈✮✫✪✬✧✼✮ ✧✓ê❣è❈✮✸èØê ✜ ✧✔ê ✧❃✭●✧✼✮✸èØê❣è ✭✸è❈✮ ❚✥❩✢❧❳❲✶❨ ❬✝❛⑤❫❵❴ ❩✔❝❞❛❞➅✢❧❪❴✬❛❤❡⑧❱❪❬✝➅❍❡❣❩❵❜❋❲✟s①❱❵❴✬❛➾❫❳❱❵❝✝t❤❱❳❺❪❛❤❡➘❜❋❩✓❴➀❺❪❛✝❬✝❛✝❴✬❱❳❲✶❨ ❬❳❺➋❫❵❴✬❛❤❜✟❛✝❴✬❛✝❬✝❝❞❛ ❲✮❛❞❡◗❲✮❡➧❲✮❩r❨ ➅❪❛✝❬❳❲✶❨ ❜✬❦➀➲✩❱❵❴✟❨ ❩✢❧❳❡✎❝②❱❪❬②❩✢❬✩❨ ❝❞❱❪❭✔❜✟❱❪③➄❨ ❭ ❨ ❛❤❡▼❩❵❜➫❧❳❲✶❨ ❭ ❨ ❲✟❦➀❜✮❧❪❬✝❝❤❲✶❨ ❩✢❬❳❡ ✪✬✫ ✭✮✪✝✯ ✰ ✱ ✲ ✳ ✴✶✵ ✷✸✯ ✹ ✺ ✻ ✼ ✹ ✽✬✺ ✴ ✴ ✳ ✰ ✰ ✻ ✾ ✲✮✿ ✳ ✹ ✳ ✼ ❀✬❁ ✼ ❂ ✱ ❃ ❄ ❅ ❆ ❆ ❇ ❈ ❉ ✻ ❊ ✹ ✳ ✼✬❅
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