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The extensions of ordinary fuzzy sets are problematic because they require decimal numbers for membership, non-membership and indecision degrees of an element from the experts, which cannot be easily determined. This will be more difficult when three or more digits' membership degrees have to be assigned. Instead, proportional relations between the degrees of parameters of a fuzzy set extension will make it easier to determine the membership, non-membership, and indecision degrees. The objective of this paper is to present a simple but effective technique for determining these degrees with several decimal digits and to enable the expert to assign more stable values when asked at different time points. Some proportion-based models for the fuzzy sets extensions, intuitionistic fuzzy sets, Pythagorean fuzzy sets, picture fuzzy sets, and spherical fuzzy sets are proposed, including their arithmetic operations and aggregation operators. Proportional fuzzy sets require only the proportional relations between the parameters of the extensions of fuzzy sets. Their contribution is that these models will ease the use of fuzzy set extensions with the data better representing expert judgments. The imprecise definition of proportions is also incorporated into the given models. The application and comparative analyses result in that proportional fuzzy sets are easily applied to any problem and produce valid outcomes. Furthermore, proportional fuzzy sets clearly showed the role of the degree of indecision in the ranking of alternatives in binomial and trinomial fuzzy sets. In the considered car selection problem, it has been observed that there are minor changes in the ordering of intuitionistic and spherical fuzzy sets. [ABSTRACT FROM AUTHOR]

The interval-valued intuitionistic fuzzy sets (IVIFSs), based on the intuitionistic fuzzy sets (IFSs), combine the classical decision method and its research and application is attracting attention. After a comparative analysis, it becomes clear that multiple classical methods with IVIFSs' information have been applied to many practical issues. In this paper, we extended the classical EDAS method based on the Cumulative Prospect Theory (CPT) considering the decision experts (DEs)' psychological factors under IVIFSs. Taking the fuzzy and uncertain character of the IVIFSs and the psychological preference into consideration, an original EDAS method, based on the CPT under IVIFSs (IVIF-CPT-EDAS) method, is created for multiple-attribute group decision making (MAGDM) issues. Meanwhile, the information entropy method is used to evaluate the attribute weight. Finally, a numerical example for Green Technology Venture Capital (GTVC) project selection is given, some comparisons are used to illustrate the advantages of the IVIF-CPT-EDAS method and a sensitivity analysis is applied to prove the effectiveness and stability of this new method. [ABSTRACT FROM AUTHOR]

Energy conservation and emission reduction are important policies vigorously promoted in China. With the continuous popularization of the concept of green transportation, electric vehicles have become a green transportation tool with good development prospects, greatly reducing the pressure on the environment and resources caused by rapid economic growth. The development status of electric vehicles has a significant impact on urban energy security, environmental protection, and sustainable development in China. With the widespread application of new energy vehicles, charging piles have become an important auxiliary infrastructure necessary for the development of electric vehicles. They have significant social and economic benefits, so it is imperative to build electric vehicle charging piles. There are many factors to consider in the scientific layout of electric vehicle charging stations, and the location selection problem of electric vehicle charging stations is a multiple-attribute group decision-making (MAGDM) problem. Recently, the Combined Compromise Solution (CoCoSo) technique and CRITIC technique have been utilized to deal with MAGDM issues. Spherical fuzzy sets (SFSs) can uncover the uncertainty and fuzziness in MAGDM more effectively and deeply. In this paper, on basis of CoCoSo technique, a novel spherical fuzzy number CoCoSo (SFN-CoCoSo) technique based on spherical fuzzy number cosine similarity measure (SFNCSM) and spherical fuzzy number Euclidean distance (SFNED) is conducted for dealing with MAGDM. Moreover, when the attribute weights are completely unknown, the CRITIC technique is extended to SFSs to acquire the attribute weights based on the SFNCSM and SFNED. Finally, the SFN-CoCoSo technique is utilized for location selection problem of electric vehicle charging stations to prove practicability of the developed technique and compare the SFN-CoCoSo technique with existing techniques to further demonstrate its superiority. [ABSTRACT FROM AUTHOR]

Cloud computing has emerged as a transformative technology in the healthcare industry, but selecting the most suitable CV ("cloud vendor") remains a complex task. This research presents a decision framework for CV selection in the healthcare industry, addressing the challenges of uncertainty, expert hesitation, and conflicting criteria. The proposed framework incorporates FFS ("Fermatean fuzzy set") to handle uncertainty and data representation effectively. The importance of experts is attained via the variance approach, which considers hesitation and variability. Furthermore, the framework addresses the issue of extreme value hesitancy in criteria through the LOPCOW ("logarithmic percentage change-driven objective weighting") method, which ensures a balanced and accurate assessment of criterion importance. Personalized grading of CVs is done via the ranking algorithm that considers the formulation of CoCoSo ("combined compromise solution") with rank fusion, providing a compromise solution that balances conflicting criteria. By integrating these techniques, the proposed framework aims to enhance the rationale and reduce human intervention in CV selection for the healthcare industry. Also, valuable insights are gained from the framework for making informed decisions when selecting CVs for efficient data management and process implementation. A case example from Tamil Nadu is presented to testify to the applicability, while sensitivity and comparison analyses reveal the pros and cons of the framework. [ABSTRACT FROM AUTHOR]