## 4 Results and Discussion
### Variation of Membership with Different Number of Interference Data  
The existence of sample contamination and incidental and instrumental data errors resulted from data measurement and analysis is inevitable, therefore, the \(x\) value of \(S_{\text{un}}\) from which could not make a determinate judgment on the processing stage among the three stages most likely exists. This type of \(x\) value, known as the interference data, would impair the reliability of the model when deciding the specific sludge-processing stage. DS evidence theory is introduced to address such problem of data impreciseness and conflict among paralleling data. To verify the performance of the model in dealing with different numbers of interference data, a group of interference data with the number below the number of the total paralleling data was introduced to one processing stage. Eighteen \(x\) values, the same with that in Section 4.1, were chosen to be the non-interference data group. The interference data group was generated through computer random selection. For Stage I, the interference data were generated from \(x\) values obtained from paralleling sludge samples of Stage I collected from 2014 to 2018. The specific values were determined by computer randomly selecting five \(x\) values whose maximal normalized memberships were \(B(S_{\text{un}})\), which could not indicate a determinate processing stage among the three stages. One interference data was brought to the six paralleling non-interference data each time, five interference data were brought in in total and the number of the total paralleling data was maintained to be six. The same operation was conducted to the other two groups \(x\) values belonging to Stage II and III, respectively. For one stage, five interference data were generated, and one data was introduced one time. The non-interference data together with the five groups \(x\) values generated by introducing one to five interference data in turn for Stage I are shown in Figure 7a. All interference data are distributed in \(S_{\text{un}}\). The corresponding integrated memberships of each fuzzy set calculated from these six groups of data are exhibited in Figure 7b. \(C(S_{\text{I}})\) are 0.99, 0.98, 0.97, 0.93, 0.85 and 0.65, and \(C(S_{\text{un}})\) are 0.01, 0.02, 0.03, 0.07, 0.15 and 0.35 with the increasing number of interference data. \(C(S_{\text{II}})\) and \(C(S_{\text{III}})\) are in a negligible range of change approximately around 0. As is shown in Figure 7b, as the number of interference data increases, the integrated membership of \(S_{\text{I}}\) goes down and that of \(S_{\text{un}}\) goes up, and \(C(S_{\text{I}})\) is the largest among the six groups. This consequence indicates that with the increasing number of interference data, the probability of this group of paralleling sludge samples belonging to Stage I declines, the uncertainty of which stage these paralleling samples are from rises, which reveals that the credibility of the five data groups with interference data descends and sample contamination and faults occurring in data measurement and analysis might appear. Furthermore, interfering \(x\) values with the number below the total paralleling data could not change the maximal integrated memberships being \(C(S_{\text{I}})\). In other words, the interference data could not play a decisive role in determining the stage affiliation of a group of paralleling samples, but could weaken the belief degree on the judgment on the processing stage affiliation being stage I. When only one non-interference data left for Stage I, \(C(S_{\text{I}})\)\(C(S_{\text{II}})\), \(C(S_{\text{III}})\) and \(C(S_{\text{un}})\) are 0.65, 0.00, 0.00 and 0.35, close to 0.60, 0.00, 0.00 and 0.40, values of \(B(S_{\text{I}})\), \(B(S_{\text{II}})\), \(B(S_{\text{III}})\) and \(B(S_{\text{un}})\) when \(x\) value is 6.98, the last non-interfering \(x\) in this data group.