## 5 A Real Case Study  
A Chinese renewable energy investment company wants to build a shopping center rooftop photovoltaic power project. In order to seek the optimal shopping mall for rooftop photovoltaic power plants, furthermore, one must judge the weight and the influence network of the criteria. A group of experts consisting of three doctorate engineers (referred to as E1, E2, E3) was constituted by the company. All three experts possess more than 15 years' working experience in solar energy investment field, and are specialized in solar photovoltaic and power grid technologies. The collaboration of the all the experts was needed, thus, a pseudo-delphi method was applied in which each expert has no interaction. Considering the development target and the investment capacity of the company, the famous influential large-scale shopping malls located in those cities, with both abundant sunshine and general policy subsidies, have been roughly screened out based on the plentitude of documents and investigation. The investigation involved several potential shopping malls located in Beijing, Shanghai, Guangzhou, Chengdu, Hangzhou, and Nanjing. The experts group met the Development and Reform Commission, the Meteorological Bureau, and the local power supply companies, in order to gather information about solar resources, city planning and construction, local solar subsidy policies, distributed solar power planning, economic assessment, and approved shopping mall rooftops for construction. There are four potential shopping malls picked out after the first filter, and they are the Golden Resources shopping mall in Beijing, Super Brand Mall in Shanghai, Deji Plaza in Nanjing, Jiangsu province, The Mixc shopping mall in Shenzhen, Guangdong province (hereafter referred to as X\({}_{1}\), X\({}_{2}\), X\({}_{3}\), X\({}_{4}\)), as shown in Figure 3.  
The alternative shopping malls geography distribution  
Firstly, based on the evaluation criteria, the influence of each criteria to the other one criteria was accessed by the experts. Then, the three experts discussed with each other and obtained a consensus about the influence of each criteria, as shown in Table 2. According to the DEMANTEL method, the weight of criteria and subcriteria was calculated based on Equations (15)-(21), and shown in Table 2. For the intuitive and simple understanding and analysis of the criteria and subcriteria, Figures 4 and 5 were drawn. As shown in Figure 4, the horizontal axis represents the importance of a criteria, while the vertical axis indicates the influence between the criteria, and the arrow is from the sender of this influence to the receiver. As we can see, the (b) economy (0.286) obtained the most importance, but was vulnerable to other criteria. The (a) architectural element and (c) climate (0.88) seemed not particularly important, however, they had significant direct impacts to the other four criteria. The (f) risk (0.188), (d) photovoltaic array (0.162), and (e) contribution (0.151) were considered of medium importance, and among them, (f) and (d) had more of an impact, while (e) received more  
Figure 3: The alternative shopping malls geography distribution. impact. Horizontal histogram clearly and intuitively shows the weight of each subcriteria in Figure 5. It is obvious that the (b1) Total investment, (b2) Total profit, and (b3). Annual rate of return acquired the highest weight, in addition to the (f4) Government subsidies reduction, (e2) Publicity effects and (d2). PV area was considered to be less but also very important. Therefore, it can be imagined that the SMPV plan alternatives which obtained high scores in these criteria are more likely to win the competition. Secondly, there are two types of criteria, one is quantitative, and the other is qualitative. On one hand, for the quantitative subcriteria, searching from the NASA atmospheric science data center, the data for c1, c2, c3 were obtained. Through using the Google earth map, the roof space data were obtained.