A Novel Extension of Fermatean Fuzzy Sets into Group Decision Making: A Study for Prioritization of Renewable Energy Technologies

Sustainable and environmental technologies for renewable energy have become more significant as countries get to consume more energy and be more sensitive to environmental issues due to regulations and public awareness. Reserves of fossil fuels are slowly being exhausted as the energy demand increases, but investments in renewable energy technologies (RETs) accelerate. The objective of this research is to offer a new robust decision framework for the assessment of RETs under an uncertain decision environment from a sustainable and environmental point of view. Evaluation of RETs driven from different natural resources is a complex problem involving the interaction of multiple criteria at the same time. Thereby, additive ratio assessment (ARAS) method, a distance-based multi-criteria decision-making (MCDM) technique, is applied to quantitatively assess candidate RETs to make use of the technique's ability to compensate for others' limitations to achieve a more convincing and comprehensive outcome. To describe the inconsistent, incomplete, ambiguous, and fuzzy information of real life, Fermatean fuzzy set (FFS) is used as an objective world setting. The interval-valued environment is a rather operational concept to cope with imprecision by considering the functions of membership and non-membership degrees in an interval and thus further capable of solving and modeling complex problems. The MCDM process can also be enriched with group decision-making (GDM) setting to combine individual decision makers' (DMs) opinions into group judgments, as well as by interval-valued FFSs (IVFF) to better simulate human opinions. Thus, this article proposes an MCDM method that integrates the IVFF–ARAS MCDM algorithm into GDM as a first in the literature and presents its application for the RETs as a decision support tool. Its feasibility and effectiveness are demonstrated in a case study for regional assessment and prioritization of RETs in Turkey.