A Large-Scale Group Decision-Making Consensus Model considering the Experts’ Adjustment Willingness Based on the Interactive Weights’ Determination
Algorithm 5
Input: The expert original evaluation matrices Qm, the number of subgroups K, the initial subject weight vector wm, and the allowed modification values and .
Output: The expert adjusted evaluation matrices, the number of iterations of CRP T, the final group consensus level GCLT and the optimal alternative xp.
Stage 1. Expert clustering.
Step 1. The DMs participated the LSGDM problem are divided into K subgroups by using Algorithm 1. Then, the subgroups G1,…, GK are obtained.
Stage 2. The weight determination.
Step 2. Calculate the DMs’ weights and the attributes’ weights for each subgroup through Algorithm 2. Then, the final weights of DMs and attributes for each subgroup can be derived. For the subgroup G1, (em ∈ Gk) and (n = 1, …, N) are obtained. It should be noted that there is an interactive process with DMs to improve the participation of DMs and better reflect the attitude of DMs. The details are shown in Step 10 of Algorithm 2.
Step 3. Compute the weights of the subgroups and the collective attributes by utilizing the Algorithm 3.
Stage 3. Obtain the unit adjustment cost cm by equation (22).
Stage 4. The CRP.
Step 4. Calculate the value of δ through equation (12), and let t = 0,
Step 5. Calculate the current consensus level GCLt, and judge whether the consensus level is acceptable. If GCLt ≥ , it means that an acceptable consensus level has been reached and go to Step 11; otherwise, let t = t + 1, and go to the Step 6.
Step 6. Determine which the subgroup and DM should be adjusted in the t-th round. The details are shown in Section 5.2.1.
Step 7. Modify the DM’s evaluation information matrix and obtain the adjusted evaluation matrix through Algorithm 4.
Step 8. Compute the consensus adjustment cost ACt in the t-th round by using equation (12).
Step 9. Compute the total adjustment cost TACt and consensus adjustment rate CARt before the t-th round by equations (13) and (14), respectively.
Step 10. Determinate whether the CRP should be terminated. If CARt-1 ≤ CARt, it should go to the Step 5; otherwise, the CRP should be terminated, let T = t − 1, and go to the Step 11.
Step 11. Output the final evaluation matrices of the DMs, the number of iterations of CRP T, and the final group consensus level GCLT. Then, go to the Step 13.
Stage 5. Selection process.
Step 12. Calculate the score s(xp)for each alternative by equation (3) and obtain the ranking of the alternative.
