Abstract
Group decision-making (GDM) implies a process of extracting wisdom from a group of experts. In this study, a novel GDM model is proposed by applying the particle swarm optimization (PSO) algorithm to simulate the consensus process within a group of experts. It is assumed that the initial positions of decision-makers (DMs) are characterized by pairwise comparison matrices (PCMs). The minimum and maximum of the entries in the same locations of individual PCMs are supposed to be the constraints of DMs’ opinions. The novelty comes with the construction of the optimization problem by considering the group consensus and the consistency degree of the collective PCM. The former is to minimize the distance between the collective PCM and each individual one. The latter is to make the collective PCM be acceptably consistent in virtue of the geometric consistency index. The fitness function used in the PSO algorithm is the linear combination of the two objectives. The proposed model is applied to solve a large-scale GDM problem arising in emergency management. Some comparisons with the existing methods reveal that the developed model has the advantages to decrease the order of an optimization problem and reach a fast yet effective solution.
Highlights
A group of experts are always considered to be much wiser than individuals to reach a reasonable solution for a complex decision-making problem [5,40]
In the phase of preference information, various preference formats could be provided by decision-makers (DMs) when evaluating their opinions on the alternatives, such as pairwise comparison matrices (PCMs) [41,51], additive reciprocal preference relations [11,35,44], linguistic preference relations [18,54], interval-valued preference relations [42,55] and others
When the particle swarm optimization (PSO) algorithm is used to achieve the consensus process, the level of consensus has been incorporated into the group decision-making (GDM) model
Summary
A group of experts are always considered to be much wiser than individuals to reach a reasonable solution for a complex decision-making problem [5,40]. From the viewpoint of the ideal consideration, the case with Q1(R) = 0 corresponding to a consistent collective PCM and the smallest value of Q2(R) is the optimal solution This means that the group of experts reach the highest consensus level while the final decision is perfectly consistent. Step 1 Using the minimum–maximum method shown in (2) and (3), an interval-valued preference relation is constructed in virtue of the above twenty matrices as follows: It is seen from the given matrix Athat the entries behave peculiar. The obtained result in [59] is in agreement with the present observation This means that the proposed model is effective to save time and reach a good consensus among DMs. At the end, it is of interest to analyze the sensitivity of the parameters p and q to the final solution of the GDM problem. This implies that the final solution of the large-scale GDM problem is not sensitive to the parameters p and q
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
