**Step 7:** End.

### **5. Comparative Analysis of Proposed Decision Framework**

This section put forwards a comparative study of the proposed aggregation operator with other operators in the IVPHFS context. In order to maintain the homogeneity of the comparison process, we analyse the proposed method with aggregation operators from References [18] and [19] which uses IVPHFEs as preference information.

Table 6 depicts the ranking order from different methods and we can see that the proposed method produces a unique ranking order compared to its counterpart. This is mainly due to the ability of the proposed aggregation operator to capture the interrelationship between multiple attributes. The consistency of the proposed method is realized by calculating the Spearman correlation coefficient [38] for each method. Figure 5 depicts the correlation plot for each method and we can infer that the proposed method is highly consistent with other state-of-the-art methods.



**Note:** DMs' weight values are considered as 0.3, 0.4 and 0.3 respectively and the attributes' weight values are considered as 0.25.

Table 7 depicts the characteristics analysis of different methods. The characteristics are adapted from the work of Liu and Teng [32].

Some strengths of the proposed method are listed below:


Some weaknesses of the proposed method are:


**Figure 5.** Corrplot for different ranking methods: Proposed vs. Others.


**Table 7.** Characteristics analysis for proposed vs. other methods.
