A fuzzy linear programming method for group decision making with additive reciprocal fuzzy preference relations

The existing methods for solving the group decision making (GDM) problems with preference relations generally include four steps: (1) estimation of missing preferences, (2) consistency and consensus reaching, (3) aggregation and (4) exploitation, which make the GDM process complicated. Relatively, very few research results focus on exploring the methods which can simplify this process to improve the efficiency. In this paper, we develop a new fuzzy linear programming method (FLPM) to deal with the GDM problems with additive reciprocal fuzzy preference relations (FPRs). The FLPM can directly produce meaningful results without the four steps. An effect index is developed to measure the decision makers (DMs)' effects in the GDM problems. Based on the FLPM and the effect index, we propose a new method to determine the DMs' weights. A step by step procedure is further proposed to deal with the GDM problems with all the developed methods, and its performance is illustrated by examples.