Journal
APPLIED MATHEMATICAL MODELLING
Volume 37, Issue 20-21, Pages 9031-9040Publisher
ELSEVIER SCIENCE INC
DOI: 10.1016/j.apm.2013.04.027
Keywords
Multiple criteria group decision making; Linguistic variable; Projection method; Incompletely known criteria weight
Funding
- Natural Science Foundation of China [70972007]
- National Sciences Foundation Committee and General Administration of Civil Aviation of China [60672180]
- Beijing Municipal Natural Science Foundation [9102015]
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Multiple criteria group decision making (MCGDM) problems have become a very active research field over the last decade. Many practical problems are often characterized by MCGDM. The aim of this paper is to develop a new approach for MCGDM problems with incomplete weight information in linguistic setting based on the projection method. Firstly, to reflect the reality accurately, a method to determine the weights of decision makers in linguistic setting is proposed by calculating the degree of similarity between 2-tuple linguistic decision matrix given by each decision maker and the average 2-tuple linguistic decision matrix. By using the weights of decision makers, all individual 2-tuple linguistic decision matrices are aggregated into a collective one. Then, to determine the weight vector of criteria, we establish a non-linear optimization model based on the basic ideal of the projection method, i.e., the optimal alternative should have the largest projection on the 2-tuple linguistic positive ideal solution (TLPIS). Calculate the 2-tuple linguistic projection of each alternative on the TLPIS and rank all the alternatives according to the 2-tuple linguistic projection value. Finally, an illustrative example is given to demonstrate the calculation process of the proposed method, and the validity is verified by comparing the evaluation results of the proposed method with that of the technique for order preference by similarity to ideal solution (TOPSIS) method. (C) 2013 Elsevier Inc. All rights reserved.
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