D-WASPAS: Addressing Social Cognition in Uncertain Decision-Making with an Application to a Sustainable Project Portfolio Problem

  • Vahid Mohagheghi
  • S. Meysam MousaviEmail author


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.


Interval-valued Pythagorean fuzzy sets (IVPFSs) Weighted aggregated sum product assessment (WASPAS) Additive ratio assessment (ARAS) Evaluation based on distance from average solution (EDAS) Complex adequate appraisal (COADAP) Sustainable project portfolio problems 



The authors would like to express their appreciation to the editor and anonymous reviewers for their valuable comments and recommendations on this article.

Authors’ Contributions

The authors of this research confirm the change on authorship based on their contributions in the revised version.

Compliance with Ethical Standards

Conflict of Interest

The authors declare that they have no conflict of interest.

Informed Consent

Informed consent was not required as no human or animals were involved.

Human and Animal Rights

This article does not contain any studies with human or animal subjects performed by any of the authors.


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Authors and Affiliations

  1. 1.Department of Industrial EngineeringShahed UniversityTehranIran

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