Fermatean fuzzy covering-based rough set and their applications in multi-attribute decision-making

Abstract

Rough set theory (RST) is a common and effective tool for data processing. In order to extend the range of data that RST and its related theories can handle, scholars have proposed many innovations on the basis of Pawlak’s model. This paper focuses on solving the multi-attribute decision-making (MADM) issue in Fermatean fuzzy environment and interval-valued Fermatean fuzzy environment by using Fermatean fuzzy β-covering rough set (CFFRS) model and interval-valued Fermatean fuzzy β-covering set (CIVFFS) model, respectively. Firstly, we give the definitions of Fermatean fuzzy β-neighborhood and interval-valued Fermatean fuzzy β-neighborhood, and then we construct CFFRS model and CIVFFRS model, respectively. Furthermore, the related properties and the complementary concepts of these two models are also discussed. Next, in order to generalize MADM approaches in Fermatean fuzzy and interval-valued Fermatean fuzzy environments, from the point of view of comparison among the advantages of the alternatives, we establish two TOPSIS methodologies based on CFFRS and CIVFFRS, respectively. Moreover, we discuss the effect of value of precision parameter β for decision-making results by two examples and conclude that the construction of fuzzy β-neighborhood is the most important influence factor in decision-making results. And then, we give a principle for the selection of the precision parameter β, and suggest the treatment when there are alternatives in decision that cannot be compared. To demonstrate the decision-making processes of novel methodologies, aiming at an electric vehicle charging stations selection issue in an India city, including Raniganj, Jamuria, Kulti, and Burnpur, the decision-making results based on CFFRS and CIVFFRS models show that Jamuria appears to be the best location to build an electric vehicle charging station. Finally, we compare the decision-making results to other existing methods, through the Spearman ranking correlation coefficient and Pearson correlation coefficient methods, we verify the effectiveness of novel approaches.