### Table 1: Parameters of the fuzzy random functions.

### Table 2: Interpolation function of the average euclidean distance of the T-transitive closure and T-transitivized relation of one hundred random fuzzy relations for each dimension from two to one hundred.

### Table 2. Neuro-fuzzy system answers

"... In PAGE 2: ...ig. 1. Voltage peaks within 10 min. periods (maximal values). Experiment results are shown in Table2 . The neuro-fuzzy system was trained with 2000 training vectors consisting of 5 random values describing the disturbances within a 10 min.... In PAGE 2: ... The lower the output value the smaller the probability of a malfunction. Test input vectors and respective outputs are summarized in Table2 . In case 2 swells were severe, so the system output is close to 1.... ..."

### Table 2: Average error rate, standard deviation of the average error rate, and average proportion of ties for different evaluation measures. Error rate was computed using a fuzziness factor of 5%. Means were computed from the error rates defined by 50 random permutations of the 21 query sets.

2000

"... In PAGE 4: ... The design also ensures that any time two methods are compared they are compared on the results of exactly the same queries. Table2 lists the mean error rate over the 50 different sets of permuted query sets for a variety of measures using a fuzziness value of 5% and ordered by decreasing error rate. The table also gives the standard deviation of the average error rate and the mean proportion of ties for each measure.... In PAGE 4: ... Figure 2 plots the average error rate over 100 trials (where each trial apos;s error rate is the average over the 50 permuted query sets) for each of the topic set sizes smaller than 50. The val- ues plotted for 50 topics are the values shown in Table2 . For all measures the average error rate decreases as the number of topics increases.... In PAGE 7: ... Both measures have a noticeably smaller error rate than any of the Prec( ) measures tested except Prec(1000). However, R-Precision does not have as much dis- crimination power as Average Precision has; Table2 shows that R-precision has one and a half times as many ties as Average Precision. This is unlikely to be strictly the result of the num- ber of points precision is being calculated at since Precision at .... ..."

Cited by 86

### Table 2: Average error rate, standard deviation of the average error rate, and average proportion of ties for different evaluation measures. Error rate was computed using a fuzziness factor of 5%. Means were computed from the error rates defined by 50 random permutations of the 21 query sets.

"... In PAGE 4: ... The design also ensures that any time two methods are compared they are compared on the results of exactly the same queries. Table2 lists the mean error rate over the 50 different sets of permuted query sets for a variety of measures using a fuzziness value of 5% and ordered by decreasing error rate. The table also gives the standard deviation of the average error rate and the mean proportion of ties for each measure.... In PAGE 4: ... Figure 2 plots the average error rate over 100 trials (where each trial apos;s error rate is the average over the 50 permuted query sets) for each of the topic set sizes smaller than 50. The val- ues plotted for 50 topics are the values shown in Table2 . For all measures the average error rate decreases as the number of topics increases.... In PAGE 7: ... Both measures have a noticeably smaller error rate than any of the Prec(a0 ) measures tested except Prec(1000). However, R-Precision does not have as much dis- crimination power as Average Precision has; Table2 shows that R-precision has one and a half times as many ties as Average Precision. This is unlikely to be strictly the result of the num- ber of points precision is being calculated at since Precision at .... ..."

### Table 8: Classification accuracy results of the hard classified fuzzy-c means classification (m=2, n=48)

2004

"... In PAGE 31: ....3.3. Sub-pixel classification The accuracy result ( Table8 ) of a hardened fuzzy-c means classification like the maps produced using standard hard classification techniques is well below the target level considered as an acceptable level for discriminating and mapping of land cover classes. The first hypothesis that this classification technique (once hardened) can be used to accurately map the different communities found in the lichen fields is thus rejected.... In PAGE 32: ...21 The third hypothesis, which questions whether a map produced by the fuzzy-c means classifier is better than randomly assigning classes to pixels, was found to be significant at the 99% confidence level ( Table8 ). Table 8: Classification accuracy results of the hard classified fuzzy-c means classification (m=2, n=48) ... ..."

### Table 5: Fuzzy and neuro-fuzzy software systems.

2003

"... In PAGE 22: ...upports independent rules (i.e., changes in one rule do not effect the result of other rules). FSs and NNs differ mainly on the way they map inputs to outputs, the way they store information or make inference steps. Table5 lists the most popular software and hardware tools based on FSs as well as on merged FSs and NNs methodologies. Neuro-Fuzzy Systems (NFS) form a special category of systems that emerged from the integration of Fuzzy Systems and Neural Networks [65].... ..."

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### Table 2 Effect of the number of fuzzy partitions of the input space on the model para- meters and the modelling accuracy

"... In PAGE 19: ... The following second-order model structure has been assumed: Li: IF CA(t) is Bi THEN CAm(t +1)= ai 1CA(t)+ai 2CA(t - 1) + bi 1Q(t)+bi 2Q(t - 1) + ki i = 1, %, p (31) Data for modelling were generated by applying 50 random step-changes. Similarly to the liquid level process, Table2 shows that the fuzzy models have a better accuracy than the linear model, and according to the fuzzy partitioning of Fig- ure 9, the MSE decreases as the number of fuzzy partitions increases. 5.... ..."

### Table 2. Influential fuzzy if-then rules for estimating the value of each market.

"... In PAGE 22: ... Thus the target output for each market was the same after the 14th round. As a result, the consequent real numbers for each market were almost the same in the seven fuzzy if-then rules in Table2 . While Table 2 was obtained from a single trial, almost the same results were obtained from other trials with different random market selection in the first two rounds.... ..."

### Table 3. Mean species composition of five clusters (i.e., forest types) from the fuzzy c-means classifier and the resulting fuzzy membership values.

"... In PAGE 7: ... The results for five clusters were among the most stable to changes in the random starting point and had entropy and partition coefficients which indicated the presence of better developed clusters than at four, six, or seven clusters. The average proportional species compositions of plots within each cluster, presented in the output of the clustering routine as cluster centers, were normalized so that the values summed to one for each species ( Table3 ). The normalized cluster centers served as the FMVs for each species on each forest type (i.... In PAGE 12: ... Also, classes with sim- ilar definitions were more likely to have high mean entropy values. Types 1 and 4 had similar species- composition definitions ( Table3 ) and it was likely that these classes were confused with each other more often than with the remaining classes.The proximity of many of the stands of these classes (Figure 8) also indic- ated that there was likely some definitional confusion.... ..."