Decision-making is an interdisciplinary area that has roots in mathematics, economics, and social science. Multiple-criteria group decision-making (MCGDM) is one of the most applicable areas of decision-making. Social cognition is involved in group decision-making. Therefore, it is necessary to address how decision makers (DMs) process and apply judgments and information during the process. In recent years, many approaches have been applied to MCGDM. As an important aspect of this process, uncertainty has led to the application of fuzzy sets. However, utilizing various decision-making approaches can result in different results and confusion among DMs. Moreover, using classic fuzzy sets and expressing degrees of belonging by crisp values has proven to be inadequate for uncertain decision-making environments. This paper presents a novel MCGDM approach, double-weighted aggregated sum product assessment (D-WASPAS), under interval-valued Pythagorean fuzzy (IVPF) uncertainty. The proposed approach applies knowledge measures to address the objective weights of criteria. Then, subjective and objective weights of criteria are aggregated to create a more appropriate weight. This approach considers three decision-making methods. In the first, an IVPF-ARAS (additive ratio assessment) method is extended to rank the alternatives. In the second, an IVPF-EDAS (evaluation based on distance from average solution) method is developed to rank the alternatives. In the third, a novel IVPF-COADAP (complex adequate appraisal) method is utilized for a third ranking. To aggregate the results, two steps are carried out using the WASPAS method. First, the results of the ranking approaches are aggregated. This process starts with computing the objective weights of the ranking approaches and aggregating the outcome with the subjective weights of the approaches. Then, the WASPAS method is applied to aggregate the obtained rankings and obtain a set of rankings for each DM. The second aggregation is utilized to aggregate the results for the DMs and reach a final set of rankings. Similarly, the subjective and objective weights of the DMs are applied in the WASPAS to aggregate the results. It should be noted that since the WASPAS method is utilized twice to aggregate the results, this approach is called D-WASPAS. A case study of the application of the proposed method shows that it is applicable to many multiple-criteria analysis and decision-making processes. Moreover, the results are more reliable because various decision-making methods are taken into consideration, and it is a last-aggregation process. Double-weighted aggregated sum product assessment offers a novel decision-making framework that is applicable in real-world decision-making situations. The proposed method is based on interval-valued Pythagorean fuzzy sets (IVPFSs), which would be especially applicable to uncertain situations. Also, it would enhance calculations of the process by offering more flexibility in dealing with uncertainty. Consequently, introducing this new decision-making framework and applying extended fuzzy sets would make the proposed method more widely applicable. The last-aggregation nature of this method avoids loss of cognitive information and assigning weights to the DMs, and the different ranking methods address the social cognition that leads to the judgments expressed and the final decisions.

中文翻译：

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D-WASPAS：在不确定的决策中解决社会认知问题，并应用于可持续项目组合问题

决策是一个跨学科领域，源于数学，经济学和社会科学。多准则小组决策（MCGDM）是决策中最适用的领域之一。社会认知参与小组决策。因此，有必要解决决策者（DM）的处理方式，并在此过程中运用判断和信息。近年来，许多方法已应用于MCGDM。作为此过程的重要方面，不确定性导致了模糊集的应用。但是，使用各种决策方法可能导致DM之间的结果不同和混乱。此外，事实证明，对于不确定的决策环境，使用经典的模糊集并用明晰的值表示归属度是不够的。本文介绍了一种新的MCGDM方法，即在区间值勾股勾股模糊（IVPF）不确定性下的双加权总和乘积评估（D-WASPAS）。提议的方法应用知识度量来解决标准的客观权重。然后，将标准的主观和客观权重相加，以创建更合适的权重。该方法考虑了三种决策方法。首先，扩展了IVPF-ARAS（加性比率评估）方法以对备选方案进行排名。在第二种方法中，开发了IVPF-EDAS（基于与平均解的距离的评估）方法对替代方法进行排名。在第三种方法中，将一种新颖的IVPF-COADAP（充分适当评估）方法用于第三种方法。为了汇总结果，使用WASPAS方法执行两个步骤。第一，排名方法的结果汇总在一起。该过程首先计算排名方法的客观权重，然后将结果与方法的主观权重相加。然后，将WASPAS方法应用于汇总获得的排名，并为每个DM获得一组排名。第二种汇总用于汇总DM的结果并达到最终排名。同样，DM的主观权重和客观权重在WASPAS中应用以汇总结果。应当注意，由于两次使用WASPAS方法来汇总结果，因此此方法称为D-WASPAS。对所提方法的应用案例研究表明，该方法适用于许多多准则分析和决策过程。此外，由于考虑了各种决策方法，因此结果更加可靠，这是最后的汇总过程。双加权总和产品评估提供了一种新颖的决策框架，适用于现实世界中的决策情况。该方法基于区间值勾股勾股模糊集（IVPFS），特别适用于不确定情况。而且，它将通过提供更大的灵活性来处理不确定性，从而增强过程的计算。因此，引入这种新的决策框架并应用扩展的模糊集将使所提出的方法更广泛地适用。此方法的最后汇总性质可避免认知信息的丢失并为DM分配权重，