*5.2. Comparison Analysis*

In ordered to compare our proposed method more effective to the existing method [56,71], we use PFDWA (PFDWGA) and PFWA (PFWGA) operators to aggregate picture fuzzy input arguments (Table 1) for the given decision matrix in Table 2 and their corresponding score values are given in Table 3 as follows:

**Table 2.** Aggregated values of the alternatives using PFWA (PFWGA) and PFDWA (PFDWGA) operators.


**Table 3.** Score values of alternatives using PFWA (PFWGA) and PFDWA (PFDWG) operators.


It follows from Table 4 that although overall rating values of the alternatives are different for these two operators, the most desirable alternative is *Q*3. In comparison with the other existing method [56,71], the ranking order of alternatives is slightly different but the optimum alternative is almost same. Thus, our proposed method is stable and can be applicable to handle different uncertain environments. It is also notified in order to compare the effectiveness of the proposed technique for MADM problems using PF-Hamacher aggregation, operators with other existing methods for MADM problems based on IF Hamacher aggregation operators [35] and bipolar fuzzy Hamacher aggregation operators [50] have some restraints and are not provided overall information about the situation. Picture fuzzy set is a more generalization of IFS. Therefore, picture fuzzy Hamacher set has provided more information (positive, neutral, negative, and refusal)-membership degrees to analyze systems of information, whereas IF-Hamacher set provides (membership, non-membership)-degree and BF-Hamacher set gives (positive, negative)-membership degree only. Therefore, the developed models PF-Hamacher set can be regarded as a further generalization of IF-Hamacher set [35]. Thus, our developed models are careful about the degrees of (positive, neutral, negative)-membership, and the soundness of the information of refusal degree of membership. Thus, existing models for IF-Hamacher set are particular cases of the proposed models of PF-Hamacher set. Hence, the developed models and algorithms in this paper not only solve MADM technique under PF-Hamacher environment, but also the MADM method with IF-Hamacher information, although the method given in [35] is only suitable for MADM problems for IF-Hamacher information.


**Table 4.** Ranking order of the alternatives.
