GRA Method for Probabilistic Linguistic Multiple Attribute Group Decision Making with Incomplete Weight Information and Its Application to Waste Incineration Plants Location Problem

Abstract

In this essay, we investigate the probabilistic linguistic multiple attribute group decision making (PL-MAGDM) with incomplete weight information. In this method, the linguistic representation developed recently is converted into probabilistic linguistic information. For deriving the weight information of the attribute, an optimization model is built on the basis of the fundamental idea of grey relational analysis (GRA), by which the attribute weights can be decided. Then, the optimal alternative is chosen through calculating largest relative relational degree from the probabilistic linguistic positive ideal solution (PLPIS) which considers both the largest grey relational coefficient (GRC) from the PLPIS and the smallest GRC form probabilistic linguistic negative ideal solution (PLNIS). In the end, a case study concerning waste incineration plants location problem is given to demonstrate the merits of the developed methods.

Keywords

• Multiple attribute group decision making (MAGDM)
• Probabilistic linguistic term sets (PLTSs)
• GRA method
• Incomplete weight information
• Waste incineration plants