Analysis and application of \(\text {r},\text {s},\text {t}\)-spherical fuzzy Aczel–Alsina aggregation operators in multiple criteria decision-making

This study focuses on the development and application of Aczel–Alsina (AA) aggregation operators (AOs) in the context of \(\textsf {r},\textsf {s},\textsf {t}\) $\mathsf{r},\mathsf{s},\mathsf{t}$ -spherical fuzzy set (SPFS) for multi-criteria decision-making (MCDM) problems. We begin by defining various \(\textsf {r},\textsf {s},\textsf {t}\) $\mathsf{r},\mathsf{s},\mathsf{t}$ -spherical fuzzy (SPF) AA operational laws and establishing their key properties. Subsequently, a series of AOs is introduced, including the \(\textsf {r},\textsf {s},\textsf {t}\) $\mathsf{r},\mathsf{s},\mathsf{t}$ -SPF weighted averaging operator, \(\textsf {r},\textsf {s},\textsf {t}\) $\mathsf{r},\mathsf{s},\mathsf{t}$ -SPF ordered weighted averaging operator, \(\textsf {r},\textsf {s},\textsf {t}\) $\mathsf{r},\mathsf{s},\mathsf{t}$ -SPF hybrid averaging operator, \(\textsf {r},\textsf {s},\textsf {t}\) $\mathsf{r},\mathsf{s},\mathsf{t}$ -SPF weighted geometric operator, \(\textsf {r},\textsf {s},\textsf {t}\) $\mathsf{r},\mathsf{s},\mathsf{t}$ -SPF ordered weighted geometric operator, and \(\textsf {r},\textsf {s},\textsf {t}\) $\mathsf{r},\mathsf{s},\mathsf{t}$ -SPF hybrid geometric operator. Each operator is discussed in relation to its specific properties, such as idempotency, monotonicity, boundedness, and commutativity. Furthermore, we utilize these operators to develop an MCDM methodology tailored to address \(\textsf {r},\textsf {s},\textsf {t}\) $\mathsf{r},\mathsf{s},\mathsf{t}$ -SPF decision-making problems, particularly when the criteria weights are completely unknown. To demonstrate the practicality and effectiveness of our approach, a case study is presented, followed by parameter analysis and a comparative study.