Multi-criteria group decision-making based on spherical fuzzy rough numbers

Multi-criteria group decision-making (MCGDM) relies heavily on the individual assessments of decision-makers, which can introduce subjectivity and uncertainty that can significantly affect the accuracy of results. Although a great deal of research has been done on managing subjectivity and uncertainty, it is still an uphill battle. Although fuzzy sets are able to capture individual uncertainty, they cannot handle the subjectivity between different decision-makers. Rough sets, on the other hand, are a realistic mathematical framework with the unique ability to handle subjective and ambiguous data without any additional modifications. Inspired by the gain of spherical fuzzy sets, which have the advantage of absorbing neutral opinions in addition to positive and negative membership degrees, can effectively represent uncertainty, and are inspired by the advantages of fuzzy rough numbers in manipulating subjectivity, this paper introduces a new concept of spherical fuzzy roughness to improve the advantages of MCGDM in managing uncertainty and subjectivity by combining the advantages of spherical fuzzy numbers and rough numbers. First, we propose a spherical fuzzy rough number to incorporate the individual judgments made by decision-makers about the importance of criteria and the potential of alternatives. We then propose an AHP-TOPSIS technique based on integrated spherical fuzzy rough number as an effective method for manipulating uncertainty and subjectivity in group decision-making settings. Furthermore, to examine the validity and effectiveness of the proposed technique, a real-life case study is conducted. This case study analyzes the bus system in Istanbul, with a particular emphasis on reducing carbon dioxide emissions and improving air quality by replacing diesel buses with electric buses. This study also involves a comprehensive comparative analysis and sensitivity analysis with the existing techniques to assess the authenticity and consistency of the proposed technique.