A novel multi-attribute group decision-making method based on the MULTIMOORA with linguistic evaluations

Multi-attribute group decision making (MAGDM) has been regarded as one of the most important branches in decision-making analysis. In the practical MAGDM problems, it is necessary to consider the connections among the different decision makers, as well as their trust levels. However, these issues are always neglected in the existing studies. In this paper, a novel method based on the MULTIMOORA (Multi-Objective Optimization by Ratio Analysis plus the Full Multiplicative From) is proposed to solve the MAGDM problems. Firstly, the weights of decision makers are determined based on the connections among different decision makers. Then, the linguistic evaluations are transformed into the form of triangular fuzzy numbers, and the normalized collective evaluations are determined, subsequently. In addition, based on the idea of classical MULTIMOORA method, the ranking result based on the ratio system, the reference point and the full multiplicative form are determined. Furthermore, an optimization model for determining the final ranking result is proposed, which has the minimum deviation with these three ranking results. Finally, an example concerning wastewater treatment is given to illustrate the feasibility and validity of the proposed method. The main contributions of this paper are: (i) the lengths of connections among these decision makers are utilized to determine the weights of different decision makers, (ii) the MULTIMOORA method is extended to solve the MAGDM problem with fuzzy linguistic evaluations and (iii) some desirable properties of the proposed method are discussed.