**6. Illustrative Example**

The following group decision making problem, which has been studied by Wu et al. [30], is taken into consideration in a quadripartitioned bipolar neutrosophic environment. Climate change in a global environment is a worrying sign. Industries have shifted their focus toward green production. A car company is eager to choose the most suitable green supplier for one of the key elements in its manufacturing process. After the pre-evaluation, four suppliers A*<sup>i</sup>* , (*i* = 1, 2, 3, 4), have been short-listed for evaluation on the basis of the concerned criteria: *a*1: is the product quality, *a*2: is technological capability, and *a*3: is pollution control. The weight vector of the concerned criteria are {*w*1, *w*2, *w*3} *<sup>T</sup>* <sup>=</sup> {0.3, 0.3, 0.4} *T* . To determine the decision information an expert is appointed to gather the criteria values for the four possible alternatives in a QBN environment which is given in Algorithm 2.

## **Algorithm 2: Decision making algorithm for the four possible alternatives in a QBN environment**

Step 1. The decision matrix [*bij*]4×<sup>3</sup> given by the expert shown in Table 1.

Step 2. The positive ideal quadripartitioned bipolar neutrosophic solution and negative ideal quadripartitioned bipolar neutrosophic solutions are calculated as: <sup>A</sup>¯<sup>∗</sup> = [h0.8, 0.6, 0.2, 0.2, <sup>−</sup>0.6, <sup>−</sup>0.6, <sup>−</sup>0.4, <sup>−</sup>0.4i, <sup>h</sup>0.9, 0.4, 0.2, 0.2, <sup>−</sup>0.5, <sup>−</sup>0.3, <sup>−</sup>0.2, <sup>−</sup>0.4i, <sup>h</sup>0.9, 0.6, 0.4, 0.3, <sup>−</sup>0.5, <sup>−</sup>0.4, <sup>−</sup>0.1, <sup>−</sup>0.3i] and <sup>A</sup><sup>∗</sup> = [h0.4, 0.2, 0.5, 0.5, <sup>−</sup>0.2, <sup>−</sup>0.3, <sup>−</sup>0.7, <sup>−</sup>0.8i, <sup>h</sup>0.6, 0.1, 0.6, 0.5, <sup>−</sup>0.1, <sup>−</sup>0.2, <sup>−</sup>0.5, <sup>−</sup>0.6i, h0.6, 0.1, 0.5, 0.7, −0.1, −0.2, −0.6, −0.8i]

Step 3. The weighted quadripartitioned similarity measure T *w* 2 (A¯<sup>∗</sup> , A*i*), *<sup>i</sup>* = 1, 2, 3, 4, and T *w* 2 (A<sup>∗</sup> , A*i*), *<sup>i</sup>* = 1, 2, 3, 4 (shown in Table 2) are computed.


**Table 1.** Decision making matrix.
