SHAHABI AND CHEN Cp,f(k)=‖ili∈Bk,=f Fp(k)=maxf E F, Cp, (k)=max (Cp, P(k)) Example 4.1. Suppose the browse-list of cluster K is A,B, G,K, Y, Z, and the values of property"Rock"for the corresponding CDs are (A, high),(B, high),(G, low),(K, medium), (Y, high), (Z, high). Because"high"has the maximum vote, the favorite PV of cluster K, FRock(K), is"high Based on these extracted favorite PVs of the cluster k, Yoda can evaluate uk(i), preference value of an item i for cluster k, by quantifying the similarity between favorite PVs and property values associated with item i. The aggregation function used to compute ux(i)is k()=max{Fp(k)×历 Example 4.2. Suppose the favorite PV of cluster K is(Rock, high), (Pop, high), (Vocal medium),(Soundtrack, medium),( Classic, low), and the item i is defined as (Rock, low), DJ. According to the above, the preference value ux(i)=max(high x low),(high x low), (medium x low), (medium x high), (low x low))=(medium x high)=0.75 4.2.2. Generating user wish-lists. During the on-line recommendation process, Yoda ag gregates the experts'wish-lists to generate the predicted user wish-list for the active user l. A fuzzy aggregation function is employed to measure and quantify the preference value vu(i)of each item i for the user u based on the user profile of user u. We use an optimized aggregation function with a triangular norm[4]. A triangular norm aggregation function g satisfy the following properties Monotonicity:g(x,y)≤g(x’,y’)ifx≤x'andy≤y Commutativity: g(r, y)=g(, x) ity: g(g(r, y).2)=g(r,g(, z)) with these properties, the query optimizer can replace the original query with a logically equivalent one and still obtain the exact same result. The optimized aggregation function we propose for Yoda is: Definition 4.6. First, experts are grouped based on their reference confidence values assigned by user G(u)=le l f is a fuzzy set F,Tue=fy Then, the preference value u(i) for item i is computed as: EB,f(i)=f×maxe()le∈Gr() ()=max{En,f()wf∈F}180 SHAHABI AND CHEN Eq. (4). Cp, f (k) = {i | i ∈ Bk , p˜i = f } (3) Fp(k) = max f | f ∈ F,Cp, f (k) = max ∀ f  ∈F {Cp, f (k)} Example 4.1. Suppose the browse-list of cluster K is {A, B, G, K, Y, Z}, and the values of property “Rock” for the corresponding CDs are {(A, high), (B, high), (G, low), (K, medium), (Y, high), (Z, high)}. Because “high” has the maximum vote, the favorite PV of cluster K, FRock(K), is “high”. Based on these extracted favorite PVs of the cluster k, Yoda can evaluate vk (i), preference value of an item i for cluster k, by quantifying the similarity between favorite PVs and property values associated with item i. The aggregation function used to compute vk (i) is: vk (i) = max{Fp(k) × p˜i} (4) Example 4.2. Suppose the favorite PV of cluster K is (Rock, high), (Pop, high), (Vocal, medium), (Soundtrack, medium), (Classic, low), and the item i is defined as {(Rock, low), (Pop, low), (Vocal, low), (Soundtrack, high), (Classic, low)}. According to the equations above, the preference value vK (i) = max {(high × low), (high × low), (medium × low), (medium × high), (low × low)} = (medium × high) = 0.75. 4.2.2. Generating user wish-lists. During the on-line recommendation process, Yoda ag￾gregates the experts’ wish-lists to generate the predicted user wish-list for the active user u. A fuzzy aggregation function is employed to measure and quantify the preference value vu(i) of each item i for the user u based on the user profile of user u. We use an optimized aggregation function with a triangular norm [4]. A triangular norm aggregation function g satisfy the following properties: Monotonicity: g(x, y) ≤ g(x , y ) if x ≤ x and y ≤ y Commuatativity: g(x, y) = g(y, x) Associativity: g(g(x, y),z) = g(x, g(y,z)) With these properties, the query optimizer can replace the original query with a logically equivalent one and still obtain the exact same result. The optimized aggregation function we propose for Yoda is: Definition 4.6. First, experts are grouped based on their reference confidence values assigned by user u. G f (u) = {e | f is a fuzzy set ∈ F, πu,e = f } (5) Then, the preference value vu(i) for item i is computed as: Eu, f (i) = f × max{ve(i) | e ∈ G f (u)} vu(i) = max{Eu, f (i) | ∀ f ∈ F} (6)