Y Jiang et al. Decision Support Systems 48(2010)470-479 Table 4 Table 6 Rules discovered from the need-rating data The final classification expert set. Rule Age Expertise CPU Battery Audio Video Rating Confidenc Classification Precondition(P) Evidence body (E) Expert Age Expertise CPU Battery Audio Video P A G 310.560 YYoMMoMM RBRR 0.310.54 00370440.19 GAA Finally, the unnecessary classification experts are pruned using the database coverage method. The database coverage threshold is set to 4, a number frequently used by other researchers 35. If a classifi- cation expert is n y to four or more records in the need-rating database, it is retained; otherwise, removed After all three phases, the M original 174 classification experts are reduced to 45 classification ex perts, which are capable of covering the 405 customers in the training set In Table 5, the classification expert R, is removed by the database coverage method because it is necessary for only two customers're- cords. As a result, the set given in Table 5 is reduced to Table 6. rules 12, [13, and r14 form classification expert R,. Overall, 174 clas- 4.3. Measure the importance of evidence bodies sification experts are derived from the 377 rules. Table 5 shows 11 of uch classification experts, which are based on data from Table 4. In After the classification experts are developed from the need-rating Table 5. 0 represents the frame of discernment for the need-rating data, the corresponding evidence bodies are evaluate data. The numbers in the last four columns represent the confidence network method. We adopt the radial basis function(RBF)neural net belief)degrees associated with each rating. For example, Ri implies work [4] to perform this task. The RBF neural network architecture, that the customers with average computer knowledge will rate In- which is designed to solve classification problems similar to the radial spiron 1525 laptop as Poor with 16% probability ' Average with 28%, basis function implemented in the software system MATLAB 7.0, has a and 'Good with 56%. A positive e shows the probability that the clas- single hidden layer with Gaussian function. Using eight data sets from sification expert cannot predict the responses of customers with such the public machine learning repository 28 to test the efficiency of the pecific precondition. As can be seen in Table 5. there are two kinds of RBF neural network for the calculation of attribute weights, we found classification experts. One is the classification experts which assign the average runtime is only 7.87% of the rough set method employed by almost all of the belief degrees to one rating. For example, classifi- CSMC[23. Furthermore, the computational results are comparable cation expert R3 implies that customers who are older than 35 and between the two methods. The high-speed neural network method need a laptop with good CPU speed will give a Good rating with 93% significantly improves the capability of the rating classifier. Following robability for Inspiron 1525 laptop. The other is the classification ex- the procedures described in Section 3.3, we obtain the weights of all rts whose ratings vary. For example, the belief degrees of classifi- evidence bodies. Table 7 shows the weights of the evidence bodies cation experts Rs are assigned more evenly to all three ratings, ' Poor, associated with the classification experts given in Table 6, where E Average, and Good, respectively. The evidence bodies given by such is the evidence body given by classification expert R, iE(2, 3,4,7, 9, classification experts provide useful information about possible cus- 10, 11) tomer ratings for the product. In the need-rating database, 20 more customers will be misclas- The second step prunes the inferior classification experts In Table 5. sified if we remove attributes CPU, audio and video from the need classification expert R6 is inferior to Ra because it gives the same rating data. This implies that the attribute set(CPU, Audio, video only classification information, but contains a more complex precondition. has a small classification power, as attested by the small weight, 20, Therefore, Rs is removed from the set of classification experts. Like- found for evidence body E1o. On the contrary, the attribute set (Age, wise, classification experts Rs and Rs are also removed because they CPU, Battery) can distinguish customers'ratings to a great extent. If w are inferior to R3 and r,, respectively remove the three attributes from the need-rating data, an additional 91 customers will receive the wrong classification. As a result, the weight of the evidence body Eg is 91. the largest of all Other weights Table 5 aton experts. Classification Precondition (P) vidence Body (E) 4.4. Construct rating classifier for potential customers Expert e Expertise CPU Battery Audio Video P A 0160.280.560 Using the entire 45 classification experts, evidence bodies, and 31 edict eights, we are able to construct a comprehensive classifier to the ratings of customers with different characteristics. For 0.31 0.560 0.13 illustration, we use the classification experts in Table 6 and the 310.5 280480240 Table 7 0280480240 The weights of the evidence bodies derived by the neural network. 31 G 0037044019 Evidence body 001000rules r12, r13, and r14 form classification expert R7. Overall, 174 clas￾sification experts are derived from the 377 rules. Table 5 shows 11 of such classification experts, which are based on data from Table 4. In Table 5, Θ represents the frame of discernment for the need-rating data. The numbers in the last four columns represent the confidence (belief) degrees associated with each rating. For example, R1 implies that the customers with average computer knowledge will rate In￾spiron 1525 laptop as ‘Poor’ with 16% probability, ‘Average’ with 28%, and ‘Good’ with 56%. A positive Θ shows the probability that the clas￾sification expert cannot predict the responses of customers with such specific precondition. As can be seen in Table 5, there are two kinds of classification experts. One is the classification experts which assign almost all of the belief degrees to one rating. For example, classifi- cation expert R3 implies that customers who are older than 35 and need a laptop with good CPU speed will give a ‘Good’ rating with 93% probability for Inspiron 1525 laptop. The other is the classification ex￾perts whose ratings vary. For example, the belief degrees of classifi- cation experts R8 are assigned more evenly to all three ratings, ‘Poor’, ‘Average’, and ‘Good’, respectively. The evidence bodies given by such classification experts provide useful information about possible cus￾tomer ratings for the product. The second step prunes the inferior classification experts. InTable 5, classification expert R6 is inferior to R4 because it gives the same classification information, but contains a more complex precondition. Therefore, R6 is removed from the set of classification experts. Like￾wise, classification experts R5 and R8 are also removed because they are inferior to R3 and R7, respectively. Finally, the unnecessary classification experts are pruned using the database coverage method. The database coverage threshold is set to 4, a number frequently used by other researchers [35]. If a classifi- cation expert is necessary to four or more records in the need-rating database, it is retained; otherwise, removed. After all three phases, the original 174 classification experts are reduced to 45 classification ex￾perts, which are capable of covering the 405 customers in the training set. In Table 5, the classification expert R1 is removed by the database coverage method because it is necessary for only two customers' re￾cords. As a result, the set given in Table 5 is reduced to Table 6. 4.3. Measure the importance of evidence bodies After the classification experts are developed from the need-rating data, the corresponding evidence bodies are evaluated using the neural network method. We adopt the radial basis function (RBF) neural net￾work [4] to perform this task. The RBF neural network architecture, which is designed to solve classification problems similar to the radial basis function implemented in the software system MATLAB 7.0, has a single hidden layer with Gaussian function. Using eight data sets from the public machine learning repository [28] to test the efficiency of the RBF neural network for the calculation of attribute weights, we found the average runtime is only 7.87% of the rough set method employed by CSMC [23]. Furthermore, the computational results are comparable between the two methods. The high-speed neural network method significantly improves the capability of the rating classifier. Following the procedures described in Section 3.3, we obtain the weights of all evidence bodies. Table 7 shows the weights of the evidence bodies associated with the classification experts given in Table 6, where Ei is the evidence body given by classification expert Ri, i∈{2, 3, 4, 7, 9, 10, 11}. In the need-rating database, 20 more customers will be misclas￾sified if we remove attributes CPU, Audio, and Video from the need￾rating data. This implies that the attribute set {CPU, Audio, Video} only has a small classification power, as attested by the small weight, 20, found for evidence body E10. On the contrary, the attribute set {Age, CPU, Battery} can distinguish customers' ratings to a great extent. If we remove the three attributes from the need-rating data, an additional 91 customers will receive the wrong classification. As a result, the weight of the evidence body E9 is 91, the largest of all. Other weights are derived similarly. 4.4. Construct rating classifier for potential customers Using the entire 45 classification experts, evidence bodies, and their weights, we are able to construct a comprehensive classifier to predict the ratings of customers with different characteristics. For illustration, we use the classification experts in Table 6 and the Table 4 Rules discovered from the need-rating data. Rule Age Expertise CPU Battery Audio Video Rating Confidence r1 * A ** * * G 0.56 r2 * A ** * * P 0.16 r3 * A ** * * A 0.28 r4 Y A ** * * P 0.31 r5 Y A ** * * A 0.50 r6 O * G * ** G 0.93 r7 M * A * ** P 0.31 r8 M * A * ** A 0.56 r9 OA G * ** G 0.93 r10 MG A * ** P 0.31 r11 MG A * ** A 0.56 r12 * G AG * * G 0.24 r13 * G AG * * P 0.28 r14 * G AG * * A 0.48 r15 * G AG * A G 0.24 r16 * G AG * A P 0.28 r17 * G AG * A A 0.48 r18 M * A G * * P 0.31 r19 M * A G * * A 0.54 r20 * * A * AGG 0.44 r21 * * A * AGA 0.37 r22 Y * * G * * G 1.00 Table 5 Examples of classification experts. Classification Expert Precondition (P) Evidence Body (E) Age Expertise CPU Battery Audio Video PAG Θ R1 *A * * * * 0.16 0.28 0.56 0 R2 YA * * * * 0.31 0.5 0 0.19 R3 O* G * * * 0 0 0.93 0.07 R4 M* A * * * 0.31 0.56 0 0.13 R5 OA G * * * 0 0 0.93 0.07 R6 MG A * * * 0.31 0.56 0 0.13 R7 *G AG * * 0.28 0.48 0.24 0 R8 *G AG * A 0.28 0.48 0.24 0 R9 M* A G * * 0.31 0.54 0 0.15 R10 ** A* A G 0 0.37 0.44 0.19 R11 Y* * G * * 0 0 1.00 0 Table 6 The final classification expert set. Classification Expert Precondition (P) Evidence body (E) Age Expertise CPU Battery Audio Video PAG Θ R2 YA * * * * 0.31 0.5 0 0.19 R3 O* G * * * 0 0 0.93 0.07 R4 M* A * * * 0.31 0.56 0 0.13 R7 *G AG * * 0.28 0.48 0.24 0 R9 M* A G * * 0.31 0.54 0 0.15 R10 ** A* A G 0 0.37 0.44 0.19 R11 Y* * G * * 0 0 1.00 0 Table 7 The weights of the evidence bodies derived by the neural network. Evidence body E2 E3 E4 E7 E9 E10 E11 Weight 37 82 82 61 91 20 53 476 Y. Jiang et al. / Decision Support Systems 48 (2010) 470–479