Using the Fuzzy Grey Relational Analysis Method in Wastewater Treatment Process Selection

Due to the variety of treatment processes, the decision to choose the best treatment process is difficult. This paper describes a fuzzy grey relational analysis (GRA) method for selection of the optimal wastewater treatment process. The rating of all alternatives and the weight of each criterion is described by linguistic variables, which can be expressed in triangular fuzzy numbers. Then, a vertex method is used to calculate the distance between two triangular fuzzy numbers. According to the concept of the GRA, a fuzzy relative relational degree is defined to determine the ranking order of all alternatives by calculating the degree of fuzzy grey relational coefficient to both the fuzzy positive ideal solution (FPIS) and fuzzy negative ideal solution (FNIS) simultaneously. Furthermore, a case study is carried out and solved by both methods (i.e., GRA and fuzzy GRA) to show the feasibility and effectiveness of the proposed method. In the case study, five anaerobic wastewater treatment alternatives are evaluated and compared against technical, economic, environmental and administrative criteria and their sub-criteria. Finally, the related results of ranking alternatives from two methods are compared with each others. By using both Fuzzy GRA and GRA, ABR process has been selected as the first priority and the best anaerobic process. The frequency count assessment of the Iran's industrial park's WWTPs which have used this method and their performance, proved the priority of this method.