New complex proportional assessment approach using Einstein aggregation operators and improved score function for interval-valued Fermatean fuzzy sets

As a generalization of the Fermatean fuzzy set, the theory of interval-valued Fermatean fuzzy set (IVFFS) is a more robust and reliable tool to address the imprecise and incomplete information in the process of multi-criteria decision making (MCDM), thus can be employed on wider range of applications. The aim of this study is to purpose a novel decision-making approach by combining two well-recognized methods, named as the criteria interaction through inter-criteria correlation (CRITIC) and the complex proportional assessment (COPRAS) with IVFFSs. In this line, to compare the interval-valued Fermatean fuzzy numbers (IVFFNs), a new score function is proposed and its feasibility in comparison with existing interval-valued Fermatean fuzzy score and accuracy functions is discussed. To combine the various IVFFNs, some interval-valued Fermatean fuzzy Einstein aggregation operators are introduced. Further, the CRITIC is utilized to derive the objective weights of attributes within IVFFS context. To prioritize the alternatives, the IVFF-COPRAS method is presented on IVFFSs settings. Later, to assess the performance quality of the developed methodology, an illustrative case study is discussed to evaluate and rank the sustainable community-based tourism (CBT) location candidates. Moreover, the comparative study and sensitivity investigation are conducted to prove that the developed framework efficiently handles the problem of sustainable CBT locations evaluation and selection problem under IVFFSs environment. The findings of this study conclude that the developed method is a systematic, more comprehensive, accurate, and structured approach in the assessment of sustainable CBT locations under uncertain environment.