Consensus Building in Group Decision Making by Yucheng Dong & Jiuping Xu

Author:Yucheng Dong & Jiuping Xu
Language: eng
Format: epub
Publisher: Springer Singapore, Singapore

(4.45)

(4.46)

The Eq. (4.46) guarantees that . Similar to the proof of Theorem 4.3, we have that . Consequently,

(4.47)

From (4.45), we obtain that

(4.48)

This completes the proof of Theorem 4.4.

The implementation of the proposed consensus reaching model requires the following two-step procedure.

Step 1: Solve the optimization model to obtain .

Step 2: Obtain the collective linguistic term , by aggregating using the TOWA operator.

Note 4.1

Let S be a linguistic term set. Theorem 4.4 shows that the proposed consensus reaching model is a mapping: , in essence. Thus, we call the proposed consensus reaching model as the OWA-based consensus operator. When the weighting vector is w and the established deviation threshold is , we denote the OWA-based consensus operator as .

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