q-Spherical fuzzy rough Einstein geometric aggregation operator for image understanding and interpretations

The combination of q-spherical fuzzy sets and rough sets has emerged as a useful paradigm for fuzzy mathematics and decision-making. The hybrid structure of q-spherical fuzzy sets and rough sets has shown to be useful in the fields of fuzzy mathematics and decision-making. The primary goal of this research is to present Einstein’s operational principles for q-spherical rough numbers (q-SFRNs). The fundamental goal of this research is to develop geometric aggregation operators (AOs), such as q-spherical fuzzy rough Einstein weighted geometric (q-SFREWG) and q-spherical fuzzy rough Einstein ordered weighted geometric (q-SFREOWG) operators. We will look at the idempotency, boundedness, and other theorems linked with the suggested AOs. Recognizing the importance of multi-criteria decision-making (MCDM) in dealing with real-world difficulties, it is important to note that traditional MCDM procedures sometimes provide contradicting outcomes. Using the proposed AOs, this study presents a robust MCDM approach designed to address picture understanding and interpretation issues inside the q-SFRS framework. In addition, a complete comparative study is carried out to assess the suggested method’s efficacy and value in comparison to existing procedures. The findings from these comparison investigations show that our developed technique outperforms current approaches. The study emphasizes the expanded capabilities of the suggested technique in resolving the complexities of picture perception and interpretation within the q-SFRS environment, bringing a potential addition to the field of decision-making and fuzzy mathematics.