## 1 Introduction
Most previous studies regarding AD have been focused on the influence of environmental factors, such as temperature, pH, volatile fatty acids, ammonia, and the feedstock composition, on the shift of methanogen community. A change from mesophilic (30-40 \({}^{\circ}\)C) to thermophilic (50-60 \({}^{\circ}\)C) condition has exerted a significant impact on the methanogen community structure [18; 19]. Improper pH might impair the microbial viability by restraining the activity of hydrolytic enzymes and producing ionic toxicity to microorganisms [20], and methanogens always require a strict range of pH for growth [21]. [PERSON] et al. [22] demonstrated the selective inhibition of ammonia on methanogens, and found the more susceptible characteristics of acetotrophic methanogens than hydrogenotrophic methanogens. Researchers have found the different effects of various feedstock, either positive or negative, on the growth of microorganisms in AD process [23; 24], and that the adding of trace elements to feedstock could facilitate the metabolism and growth of methanogens [25]. As for the research on thermal hydrolysis pretreatment, much attention has been payed to the effect of temperature and heating time on the efficiency of hydrolysis and biogas yields. The optimal temperature and heating time vary greatly from 160 to 180\({}^{\circ}\)C and 30 to 60 mins, respectively [26; 27; 28; 29; 30]. [PERSON] et al. [31] further confirmed thermal hydrolysis changed the composition and species abundance of the microbial community compared with the un-pretreated one. However, study on the shift of methanogen community in a sludge-treatment process has not been investigated yet. For a wastewater treatment plant, a clear characterization of the shift of methanogen community could reflect the efficiency and environmental condition of different processing stage, which could provide workers an advisable instruction to regulate the sludge-treatment process. In each sludge-processing stage, the structure of methanogen community is unique and in a relative stable range of change because of the heterogeneous and relatively steady environmental condition each stage provides. Therefore, the boundary of the methanogen community structure between two processing stages could not be such clear. Furthermore, the data error caused by sample contamination and faultsoccurring in data measurement and analysis processes has not been fully taken into consideration when analyzing the microbial information in previous research. Although paralleling samples were collected to weaken the data error, the method to process the paralleling data is just taking the average value. If the paralleling data deviated extremely, the average value could not represent the authentic one. Fuzzy sets are good at describing the vagueness of a certain phenomenon and uncertainty caused by data error [32; 33; 34], and Dempster-Shafer (DS) evidence theory is adept at fusing imprecise and conflict data from multi-sources [35; 36]. Both theories are combined to resolve the problem of the uncertain boundary of the methanogen community structure between two sludge-processing stages and data error generated among paralleling data. This paper aims to propose a membership-fusing model combing fuzzy sets and DS evidence theory to properly characterize the shift of methanogen community in different processing stages of a three-stage sludge-treatment process and reasonably determine which stage the tested paralleling sludge samples most likely come from by measuring the shift of methanogen community. The organization of this paper is as follows: In Section 2, the three-stage sludge-treatment process is abstracted and the main functional methanogens able to characterize the shift of methanogen community are selected. Then the membership-fusing model is established based on fuzzy sets and DS evidence theory.