Complex Fermatean fuzzy sets (CFFSs) integrate the ideas of complex fuzzy sets and Fermatean fuzzy sets, where the membership, non-membership, and hesitancy degrees are all complex numbers, allowing the express uncertain information more flexibly and comprehensively. However, how to reasonably measure the discrepancies between CFFSs in decision-making remains an open task. This paper presents a series of new distance measures of CFFSs and their weighted versions based on Hamming, Euclidean, Hausdorff, and Hellinger distances. On this basis, we explore some outstanding properties that the proposed measures satisfy (i.e., boundedness, nondegeneracy, symmetry, and triangular inequality) and demonstrate their effectiveness through several examples. Furthermore, we design a decision-making algorithm as well as a clustering algorithm based on the proposed measures and verify the performance of the proposed measures through several applications.

There should be some improvements to increase the performance of Metaverse investments. However, businesses need to focus on the most important actions to provide cost effectiveness in this process. In summary, a new study is needed in which a priority analysis is made for the performance indicators of Metaverse investments. Accordingly, this study aims to evaluate the main determinants of the performance of the metaverse investments. Within this context, a novel model is created that has four different stages. The first stage is related to the prioritizing the experts with artificial intelligence-based decision-making method. Secondly, missing evaluations are estimated by expert recommendation system. Thirdly, the criteria are weighted with Quantum picture fuzzy rough sets-based (QPFR) M-Step-wise Weight Assessment Ratio Analysis (SWARA). Finally, investment decision-making priorities are ranked by QPFR VIKOR (Vlse Kriterijumska Optimizacija Kompromisno Resenje). The main contribution of this study is the integration of the artificial intelligence methodology to the fuzzy decision-making approach for the purpose of computing the weights of the decision makers. Owing to this condition, the evaluations of these people are examined according to their qualifications. This situation has a positive contribution to make more effective evaluations. Organizational effectiveness is found to be the most important factor in improving the performance of metaverse investments. Similarly, it is also identified that it is important for businesses to ensure technological improvements in the development of Metaverse investments. On the other side, the ranking results indicate that regulatory framework is the most critical alternative in this regard.

Currently, many studies have developed distance or divergence measures between intuitionistic fuzzy sets (IFSs) and interval-valued fuzzy sets (IvFSs). As a generalization of IFSs, picture fuzzy sets (PFSs) provide a more nuanced representation of uncertain and ambiguous information. Interval-valued picture fuzzy sets (IvPFSs) combine the concepts of IvIFSs and PFSs, providing a highly effective means of representing and processing uncertain, ambiguous and incomplete information. How to better measure the differences between PFSs and IvPFSs is still an open issue. This paper proposes some novel α-divergence measures for PFSs and IvPFSs, respectively. We demonstrate the basic properties of the proposed divergence measures, including non-negativity, non-degeneracy and symmetry. Besides, we analyze some special cases of the proposed divergence measures that degenerate into or are related to several well-known divergences. Then, we construct some numerical examples to demonstrate the effectiveness of the proposed measures concerning existing measures. Finally, the proposed α-divergence measures are applied to pattern recognition, multi-attribute decision-making (MADM) and clustering, demonstrating that these measures possess a high confidence level and can produce trustworthy results, especially in comparable situations.

The most essential criteria should be determined in the selection of the suitable energy transition technologies due to budget deficit problem. Therefore, it is necessary to identify the most important criteria in energy transition technology selection. Therefore, a new study is needed to determine the most prominent issues in the correct selection of energy transition technologies. The purpose of this study is to identify the most appropriate energy transition technology alternative. Within this framework, a novel artificial intelligence (AI)-based fuzzy decision-making model has been presented. In the first part, the experts are prioritized by the help of AI methodology. In the next section, missing evaluations of energy transition technology investments are estimated via expert recommender system. Thirdly, the weights of the criteria for energy transition technology selection are computed by quantum picture fuzzy rough sets (QPFR) M-Stepwise Weight Assessment Ratio Analysis (SWARA). At the final stage, selected energy transition technology alternatives are ranked via QPFR-Vlse Kriterijumska Optimizacija Kompromisno Resenje (VIKOR). The main contribution of this study is the integration of AI technique to the proposed model. Similar to this issue, using M-SWARA methodology in the process of criteria weighting increases the quality of the findings. This methodology helps to consider the impact relation map of the criteria. The findings demonstrate that the most important factor is cost-effectiveness of energy transition. Similarly, it is also found that the local ecosystem is the second most significant issue. On the other side, the ranking results denote that compact renewable systems for small scale production is the most optimal solution of energy transition technology alternatives.