A Large-Scale Group Decision-Making Consensus Model considering the Experts’ Adjustment Willingness Based on the Interactive Weights’ Determination
Algorithm 3
The weight determination for each subgroup.
Input: The cluster results G1, G2, …, GK, and the satisfaction degree for each DM.
Output: The final weight value for each subgroup.
Step 1. Calculate the initial weight for each subgroup according to the number of the DMs in the subgroup. Obviously, the larger the number of the subgroup, the higher the weight value. The calculation equation is that:
where represents the initial weight value of the subgroup Gk, and satisfies 0 ≤ ≤ 1, and = 1.
Step 2. Compute the mean value and variance of satisfaction degree for each subgroup. The mean value and variance of satisfaction degree of the subgroup is denoted as and , respectively, and the calculation formulas are shown as follows. ,
Step 3. Define and calculate the harmonious degree for each subgroup. Apparently, the harmonious degree is related not only to the mean value of the satisfaction degree but also to the variance in a subgroup. The calculation equation of the harmonious degree of the subgroup Gk is presented as follows.
The properties of the harmonious degree is introduced as follows for the subgroup Gk:
(a)
The value of meets condition 0 ≤ ≤1.
(b)
= when = 0.
(c)
≤ at any time.
(d)
It increases monotonically for , and decreases for .
Step 4. Update the weight for each subgroup according to the harmonious degree. Obviously, the greater the harmonious degree, and the weight of the subgroup should be improved to some extent. The updating formula is performed as follows.
where represents the importance of harmonious degree in the updating weight process. The value of is considered as the final weight value for each subgroup.
