Abstract Considering classical set theory, asymmetric and ambiguous information management is challenging. In fuzzy set (FS) theory, Aczel-Alsina aggregation operators (AOs) are new developments. However, when experts try to use classical set theory for rough fuzzy structures, these concepts fail to handle such values, as fuzzy irregular frameworks use upper and lower approximation spaces. However, data loss is possible when a Pythagorean FS (PyFS) is enclosed, but the issue can be solved by a Pythagorean fuzzy (PyF) rough (PyFR) set. By taking motivation from these newly introduced operational laws, PyFR Aczel-Alsina (PyFRAA), T-conorm (TCNM), and T-norm (TNM), this article firstly introduces the PyFRAA operations for PyF rough values. Secondly, based on newly developed Aczel-Alsina (AA) operations, we have proposed PyFRAA power-weighted averaging (PyFRAAPWA) and PyFRAA power-weighted geometric (PyFRAAPWG) AOs. These AOs help aggregate asymmetric and awkward data in real-life issues. The suggested AOs in medical diagnosis and multi-attribute group decision-making (MAGDM) are suitable techniques that can help in medical diagnosis and decision-making theory. We established a real-life numerical example with a detailed algorithm to highlight the effectiveness and universality of the presented AOs in the medical sciences and the selection of the finest treatment method. To deliberate the diversity and significance of the developed AOs, we offer a comparative investigation with the present AOs.
Ali et al. (Thu,) studied this question.
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