Yi-Shin Chen and Cyrus shahabi and quantify the preference value vQi of each item i for the user-based on the user profile of user-. We use an optimized aggregation function with triangular norm [19. A triangular norm aggregation function g satisfy the following properties Monotonicity:g(xr,y)≤g(x,y)ifx≤ ' and y≤y Commutativity: g(a, y)=g(y, a Associativity: g(g(, y), a) =g(a, with these properties, the query optimizer can replace the original query with a logically equivalent one and still obt ain the exact same result. The optimized aggregation function we propose for Yoda Definition 5. First, experts are grouped based on their reference confidence values assigned by user GA()=el f is a fuzzy set g F, TO=f) Then, the preference value v@i) for item ted as EOA(i)=f x max ve(i) eg GA(-) vQi= max(EoA(i)vf g FI Basically, this aggregation function partitions the preference values into different subgroups according to the confidence values of the expe Subsequently, the system maintains a list of maximum preference values for all subgroups. Finally, the system computes the preferences of all items in he user wish-list by iterating through all subgroups. As compared to a naive weighted aggregation function with time complexity C(E‖×‖4)( where ell is the number of experts in the system) the complexity of the proposed gregation function is O(‖F‖×‖41)=O(4), where‖l‖ is a small constant number representing the number of fuzzy terms To reduce the time complexity of generating the user wish-lists further, we apply a cut-off point on the expert wish-lists. Each shorten wish-list in- ludes the N best-ranked items according to their preference values for the corresponding expert. In [19, Fagin has proposed an optimized algorithm, the Ao algorithm, to retrieve N best items from a collection of subsets of items with time complexity proportional to N rather than total number of items. Here, by taking the subgroups of items(as described above) as the subsets, the Ao algorithm can be incorporated into Yoda. applying the Ao algorithm to generate a user wish-list with cut-off point N, we reduce the time complexity to O(F‖×‖N‖)=O(N), where‖|N‖<‖4‖ Since our aggregation function is in triangular norm form, it satisfies the require❷ ➳✸❵ ❸❡❜✦✇♥❵❚①❤✕✇♥❳✽❚✵❬✍❚❉❪①❤✈❝✦❩❇♠♥❞❍❜✦✇❉❬✍✇❉❬✍➝♥❵ ❏✦❋▲❑áÑ♥❖▲❏✦❋♥❒P❃❮➊▼✿❒P❈❊■①ß❊◆P■✣❮➊■✍◆P■✍❋▲➮✣■✵Ò❲❏✦Ï❖❊■ ✥✛✴✜ ✔ ✣✡➱✦❮✸■❦❏❛➮✽❈✢❃❒P■✍✃ ✔✱❮➊➱❛◆➽❒P❈❊■①❖▲◗❭■✍◆ ✙à❘▲❏❛◗❭■❦❑ ➱❛❋➢❒P❈❊■➽❖▲◗❭■✍◆✱ß❊◆P➱✥￾▲Ï■❄➱✦❮✈❖▲◗❭■✍◆ ✙✕ä⑧ûá■➽❖▲◗❭■➽❏✦❋☞➱❛ß⑧❒P❃✃✵❃❰✍■❦❑➧❏✦Ð❛Ð❛◆P■✍Ð♥❏❲❒P❃➱❛❋✵❮➊❖❊❋▲➮❫❒P❃➱❛❋☞ç✱❃❒P❈ ❏✧❒P◆P❃④❏✦❋❊Ð❛❖❊Ï④❏✦◆✸❋❊➱❛◆P✃❬✯ ✱✶❯✞✸❡ä Þ ❒P◆P❃④❏✦❋❊Ð❛❖❊Ï④❏✦◆✐❋❊➱❛◆P✃ ❏✦Ð❛Ð❛◆P■✍Ð♥❏❲❒P❃➱❛❋①❮➊❖❊❋▲➮❫❒P❃➱❛❋✁￾➧◗P❏❲❒P❃④◗❇❮➊▼①❒P❈❊■ ❮➊➱❛Ï Ï➱❲ç✱❃❋❊Ð✵ß❊◆P➱❛ß➩■✍◆❭❒P❃■❦◗✄✂ ✿✿➱❛❋❊➱✦❒P➱❛❋❊❃④➮✣❃❒❇▼✴✂✂￾❀✜ ✤✎✔☎✄❋✣✝✆✞￾❀✜ ✤✠✟ ✔☎✄✡✟ ✣ö❃❮ ✤☛✆ ✤ ✟ ❏✦❋▲❑✁✄☞✆✌✄ ✟ ●❍➱❛✃✵✃✧❖▲❏❲❒✽❏❲❒P❃Ò❉❃❒❇▼✴✂✍￾❀✜ ✤✎✔☎✄❋✣ ✏✎￾❀✜✏✄✮✔✦✤✴✣ Þ◗P◗❭➱⑧➮✣❃④❏❲❒P❃Ò❉❃❒❇▼✴✂✑￾❀✜✒￾❀✜ ✤✎✔☎✄❋✣ ✔✔✓✙✣ ✏✎￾❀✜ ✤✎✔✕￾❀✜✏✄✮✔✔✓✙✣ ✣ û✫❃❒P❈➢❒P❈❊■❦◗❭■✡ß❊◆P➱❛ß➩■✍◆❭❒P❃■❦◗✍❐✦❒P❈❊■➽Ñ♥❖❊■✍◆P▼✮➱❛ß⑧❒P❃✃✵❃❰✍■✍◆✸➮✍❏✦❋①◆P■✍ß❊Ï④❏❛➮✣■✖❒P❈❊■✡➱❛◆P❃Ð❛❃❋▲❏✦Ï➩Ñ♥❖❊■✍◆P▼ ç✱❃❒P❈➯❏✿Ï➱❛Ð❛❃④➮✍❏✦Ï Ï▼á■❦Ñ♥❖❊❃Ò❲❏✦Ï■✍❋♥❒✧➱❛❋❊■➧❏✦❋▲❑ ◗❇❒P❃ Ï Ï✐➱❛❘⑧❒✽❏✦❃❋ ❒P❈❊■➧■✣é❊❏❛➮❫❒✮◗P❏✦✃✵■➢◆P■❦◗❭❖❊Ï❒❦ä②æ✸❈❊■ ➱❛ß⑧❒P❃✃✵❃❰✍■❦❑✝❏✦Ð❛Ð❛◆P■✍Ð♥❏❲❒P❃➱❛❋✵❮➊❖❊❋▲➮❫❒P❃➱❛❋✿ç✐■➽ß❊◆P➱❛ß➩➱♥◗❭■✡❮➊➱❛◆✸❂✼➱⑧❑❊❏✵❃④◗✄✂ ✏☞➚✒✑■▼❍❑❏✶❍❾➹✆▼✗✖ ✎ ❃✕❃ ◆✽◗❇❒❦❐❲■✣é⑧ß➩■✍◆❭❒✽◗✟❏✦◆P■✸Ð❛◆P➱❛❖❊ß➩■❦❑✛❘▲❏❛◗❭■❦❑✧➱❛❋✧❒P❈❊■✍❃ ◆✼◆P■✣❮➊■✍◆P■✍❋▲➮✣■✸➮✣➱❛❋❆￾➩❑⑧■✍❋▲➮✣■ Ò❲❏✦Ï❖❊■❦◗✱❏❛◗P◗❭❃Ð❛❋❊■❦❑➧❘❉▼➢❖▲◗❭■✍◆✎✙✕ä ❃✫ ✜ ✙❀✣ ✏ ✒ ✝✚✖✱✮✿❃④◗✖❏✧❮➊❖❊❰✍❰✍▼☞◗❭■✣❒ ✜✙✜✚✔ ☎✛ ✓ ✕ ✏✯✮ ✘ ✜ ✁ ✣ æ✸❈❊■✍❋✂❐❉❒P❈❊■❣ß❊◆P■✣❮➊■✍◆P■✍❋▲➮✣■➽Ò❲❏✦Ï❖❊■✱✥✛✆✜ ✔ ✣❍❮➊➱❛◆✱❃❒P■✍✃ ✔❍❃④◗✱➮✣➱❛✃✵ß❊❖⑧❒P■❦❑✝❏❛◗✄✂ ￾✛ ✓ ✫ ✜ ✔ ✣ ✏ ✮☞❅☞✃①❏❲é ✒ ✥✕ ✜ ✔ ✣✎✖✰✝ ✜ ❃✫ ✜ ✙❀✣ ✘ ✥✛✴✜ ✔ ✣ ✏ ✃①❏❲é ✒￾✛ ✓ ✫ ✜ ✔ ✣✎✖ ❇❈✮ ✜✆✜✘ ✜✪✵ ✣ ✘✸❏❛◗❭❃④➮✍❏✦Ï Ï▼❛❐▲❒P❈❊❃④◗❣❏✦Ð❛Ð❛◆P■✍Ð♥❏❲❒P❃➱❛❋☞❮➊❖❊❋▲➮❫❒P❃➱❛❋áß▲❏✦◆❭❒P❃❒P❃➱❛❋▲◗✡❒P❈❊■✵ß❊◆P■✣❮➊■✍◆P■✍❋▲➮✣■✮Ò❲❏✦Ï❖❊■❦◗❄❃❋♥❒P➱ ✬✣✜ ✬✧❑⑧❃â➤■✍◆P■✍❋♥❒❣◗❭❖❊❘❊Ð❛◆P➱❛❖❊ß▲◗❄❏❛➮✍➮✣➱❛◆✽❑⑧❃❋❊Ð➢❒P➱➧❒P❈❊■①➮✣➱❛❋❆￾➩❑⑧■✍❋▲➮✣■✮Ò❲❏✦Ï❖❊■❦◗❄➱✦❮❍❒P❈❊■✵■✣é⑧ß➩■✍◆❭❒✡✝♥ä ❆❉❖❊❘▲◗❭■❦Ñ♥❖❊■✍❋♥❒PÏ▼❛❐❊❒P❈❊■✧◗❭▼⑧◗❇❒P■✍✃ ✃①❏✦❃❋♥❒✽❏✦❃❋▲◗✡❏✵Ï ❃④◗❇❒✡➱✦❮✟✃①❏❲é⑧❃✃✧❖❊✃ ß❊◆P■✣❮➊■✍◆P■✍❋▲➮✣■❣Ò❲❏✦Ï❖❊■❦◗✸❮➊➱❛◆ ❏✦Ï Ï✐◗❭❖❊❘❊Ð❛◆P➱❛❖❊ß▲◗✍ä ❃✕❃❋▲❏✦Ï Ï▼❛❐✈❒P❈❊■➧◗❭▼⑧◗❇❒P■✍✃ ➮✣➱❛✃✵ß❊❖⑧❒P■❦◗✛❒P❈❊■➢ß❊◆P■✣❮➊■✍◆P■✍❋▲➮✣■❦◗✛➱✦❮✖❏✦Ï Ï❍❃❒P■✍✃①◗✧❃❋ ❒P❈❊■✡❖▲◗❭■✍◆✼ç✱❃④◗❭❈⑧❅❡Ï ❃④◗❇❒❍❘❉▼✮❃❒P■✍◆✽❏❲❒P❃❋❊Ð➽❒P❈❊◆P➱❛❖❊Ð❛❈①❏✦Ï Ï➩◗❭❖❊❘❊Ð❛◆P➱❛❖❊ß▲◗✍ä Þ◗❍➮✣➱❛✃✵ß▲❏✦◆P■❦❑✧❒P➱✧❏❣❋▲❏✦❃Ò❛■ ç✐■✍❃Ð❛❈♥❒P■❦❑ ❏✦Ð❛Ð❛◆P■✍Ð♥❏❲❒P❃➱❛❋✢❮➊❖❊❋▲➮❫❒P❃➱❛❋➯ç✱❃❒P❈ ❒P❃✃✵■✝➮✣➱❛✃✵ß❊Ï■✣é⑧❃❒❇▼ ☛❂✜❂✬ ￾ ✬ ❅ ✬✗✍✼✬✄✣ ✜➊ç✱❈❊■✍◆P■ ✬ ￾ ✬✡❃④◗✐❒P❈❊■➽❋❉❖❊✃✧❘➩■✍◆✖➱✦❮✕■✣é⑧ß➩■✍◆❭❒✽◗✸❃❋➧❒P❈❊■✛◗❭▼⑧◗❇❒P■✍✃✣✼❒P❈❊■✛➮✣➱❛✃✵ß❊Ï■✣é⑧❃❒❇▼➢➱✦❮✈❒P❈❊■❣ß❊◆P➱❛ß➩➱♥◗❭■❦❑ ❏✦Ð❛Ð❛◆P■✍Ð♥❏❲❒P❃➱❛❋✖❮➊❖❊❋▲➮❫❒P❃➱❛❋✛❃④◗❀☛❂✜❂✬✣✜ ✬✆❅✁✬✗✍✼✬✄✣✲✏ ☛❂✜❂✬✗✍✼✬✄✣❫❐❦ç✱❈❊■✍◆P■ ✬✣✜ ✬✕❃④◗✈❏✖◗❭✃①❏✦Ï Ï♥➮✣➱❛❋▲◗❇❒✽❏✦❋♥❒ ❋❉❖❊✃✧❘➩■✍◆✱◆P■✍ß❊◆P■❦◗❭■✍❋♥❒P❃❋❊Ð✧❒P❈❊■❣❋❉❖❊✃✧❘➩■✍◆✖➱✦❮✈❮➊❖❊❰✍❰✍▼➢❒P■✍◆P✃①◗✍ä æ✈➱☞◆P■❦❑⑧❖▲➮✣■✮❒P❈❊■✮❒P❃✃✵■➢➮✣➱❛✃✵ß❊Ï■✣é⑧❃❒❇▼✿➱✦❮✐Ð❛■✍❋❊■✍◆✽❏❲❒P❃❋❊Ð➧❒P❈❊■✵❖▲◗❭■✍◆➽ç✱❃④◗❭❈⑧❅❡Ï ❃④◗❇❒✽◗❄❮➊❖❊◆❭❒P❈❊■✍◆❦❐ ç✐■✮❏✦ß❊ß❊Ï▼å❏➧➮✣❖⑧❒❭❅❡➱✦âàß➩➱❛❃❋♥❒➽➱❛❋å❒P❈❊■✮■✣é⑧ß➩■✍◆❭❒❄ç✱❃④◗❭❈⑧❅❡Ï ❃④◗❇❒✽◗✍ä ✟❍❏❛➮✽❈å◗❭❈❊➱❛◆❭❒P■✍❋åç✱❃④◗❭❈⑧❅❡Ï ❃④◗❇❒➽❃❋⑧❅ ➮✣Ï❖▲❑⑧■❦◗✡❒P❈❊■✙✘✺❘➩■❦◗❇❒❭❅❡◆✽❏✦❋❊Ó❛■❦❑✿❃❒P■✍✃①◗➽❏❛➮✍➮✣➱❛◆✽❑⑧❃❋❊Ð①❒P➱➧❒P❈❊■✍❃ ◆➽ß❊◆P■✣❮➊■✍◆P■✍❋▲➮✣■✧Ò❲❏✦Ï❖❊■❦◗✡❮➊➱❛◆❄❒P❈❊■ ➮✣➱❛◆P◆P■❦◗❭ß➩➱❛❋▲❑⑧❃❋❊Ð✿■✣é⑧ß➩■✍◆❭❒❦ä✕èq❋✫✯ ✱✶❯✞✸❡❐ ❃▲❏✦Ð❛❃❋ ❈▲❏❛◗✛ß❊◆P➱❛ß➩➱♥◗❭■❦❑à❏✦❋à➱❛ß⑧❒P❃✃✵❃❰✍■❦❑ ❏✦ÏÐ❛➱❛◆P❃❒P❈❊✃✝❐ ❒P❈❊■✛✚✢✜✝❏✦ÏÐ❛➱❛◆P❃❒P❈❊✃✝❐✈❒P➱✢◆P■✣❒P◆P❃■✍Ò❛■☞✘✯❘➩■❦◗❇❒✵❃❒P■✍✃①◗✧❮➊◆P➱❛✃ ❏✢➮✣➱❛Ï Ï■❦➮❫❒P❃➱❛❋ ➱✦❮❄◗❭❖❊❘▲◗❭■✣❒✽◗✧➱✦❮ ❃❒P■✍✃①◗➽ç✱❃❒P❈á❒P❃✃✵■①➮✣➱❛✃✵ß❊Ï■✣é⑧❃❒❇▼åß❊◆P➱❛ß➩➱❛◆❭❒P❃➱❛❋▲❏✦Ï✈❒P➱☛✘✳◆✽❏❲❒P❈❊■✍◆✡❒P❈▲❏✦❋á❒P➱✦❒✽❏✦Ï②❋❉❖❊✃✧❘➩■✍◆❣➱✦❮ ❃❒P■✍✃①◗✍ä■✦✖■✍◆P■❛❐✕❘❉▼á❒✽❏✦Ó❉❃❋❊Ð✿❒P❈❊■✝◗❭❖❊❘❊Ð❛◆P➱❛❖❊ß▲◗❣➱✦❮✖❃❒P■✍✃①◗ ✜❾❏❛◗✧❑⑧■❦◗P➮✣◆P❃❘➩■❦❑ ❏✦❘➩➱❲Ò❛■✤✣❣❏❛◗✛❒P❈❊■ ◗❭❖❊❘▲◗❭■✣❒✽◗✍❐⑧❒P❈❊■✣✚✢✜✧❏✦ÏÐ❛➱❛◆P❃❒P❈❊✃ ➮✍❏✦❋☞❘➩■✛❃❋▲➮✣➱❛◆Pß➩➱❛◆✽❏❲❒P■❦❑➧❃❋♥❒P➱✵❂✼➱⑧❑❊❏✥✤tä Þß❊ß❊Ï▼❉❃❋❊Ð①❒P❈❊■✦✚✢✜ ❏✦ÏÐ❛➱❛◆P❃❒P❈❊✃✻❒P➱åÐ❛■✍❋❊■✍◆✽❏❲❒P■➢❏å❖▲◗❭■✍◆✧ç✱❃④◗❭❈⑧❅❡Ï ❃④◗❇❒✧ç✱❃❒P❈➯➮✣❖⑧❒❭❅❡➱✦â⑩ß➩➱❛❃❋♥❒✙✘à❐✈ç✐■➢◆P■❦❑⑧❖▲➮✣■➢❒P❈❊■ ❒P❃✃✵■✛➮✣➱❛✃✵ß❊Ï■✣é⑧❃❒❇▼①❒P➱ ☛❂✜❂✬✣✜ ✬ ❅ ✬✧✘✥✬✄✣✲✏✯☛❂✜❂✬✧✘✥✬✄✣❫❐⑧ç✱❈❊■✍◆P■ ✬✧✘✥✬✩★ ✬✗✍✼✬❲ä ✪ ❜✦❵❚♥♦✽❳✼❥❦♠❛❩②❬✍❨❦❨✍❩❇❳✽❨t❬✣❱❇❵❥❦❚✛✉④♠♥❚♥♦P❱❇❵❥❦❚❣❵ ❞✕❵❚❄❱q❩❇❵ ❬✍❚♥❨❦♠♥③ ❬✣❩②❚♥❥✍❩❇❢✫✉④❥✍❩❇❢✵⑤t❵ ❱②❞❇❬✣❱❇❵ ❞❡➦❉❳✽❞✈❱❇✇♥❳②❩❇❳☞☛❲♠♥❵❩❇❳P❸ ❢❣❳✽❚❲❱❇❞②❥✍✉❁❱❇✇♥❳✬✫✝✭✱❬✍③❨❦❥✍❩❇❵❱❇✇♥❢✵➟